modelling, design and analysis of innovative thermal energy storage...
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Università degli Studi di Cagliari
DOTTORATO DI RICERCA
Progettazione Meccanica
Ciclo XXVIII
Modelling, design and analysis of innovative
thermal energy storage systems using PCM
for industrial processes, heat and power
generation.
ING-IND/09
Author Arena Simone
PhD coordinator Prof. Mandas Natalino
Supervisor Prof. Cau Giorgio
Esame finale anno accademico 2014 – 2015
i
ii
Acknowledgements
First of all, I would like to thank my supervisor, Prof. Giorgio Cau, for the possibility of
undertaking this PhD, and for his support and advice during these three years at the
Department of Mechanical, Chemical and Materials Engineering (DIMCM), University of
Cagliari, Italy.
I wish to remember Prof. Chiara Palomba, who left us prematurely, for her fundamental support
and advices at the beginning my research project.
I would also like to thank my Spanish supervisor, Dr. Loreto Valenzuela, for her help during my
stay at the Plataforma Solar de Almeria (Ciemat) - Almeria, Spain.
Another special thanks to Prof. Luisa Cabeza for hosting me in Grea Innovació Cuncurrent,
University of Lleida.
Thanks to my colleagues at the Department of Mechanical, Chemical and Materials Engineering,
the PSA researcher group and the Grea researcher group, for the wonderful time spent together
and for being good friends.
Special thanks to Federica for the love, joy and constant support she give me during this
experience.
Last, I am grateful to my family, who has always believed in me, and this has permitted me to be
what I am, and therefore to reach this important goal.
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Abstract
The topic of this PhD thesis is framed on the study and the analysis of thermal energy storage
(TES) systems based on phase change materials (PCM) to be used as a back-up for intermediate
temperature applications (up to 250 °C). The work is divided in two part: the first part presents the
development of numerical models of the latent heat thermal energy storage (LHTES) devices.
Different models are developed by means of a 2D and 3D numerical simulation codes specifically
implemented in the COMSOL Multiphysics environment. Design of LHTES requires knowledge
of the heat transfer process within them, as well as the phase change behaviour of the PCM used.
For simulate the PCM, two approaches are used: the first approach takes only into account heat
transfer by conduction during the entire process, also when the PCM is in the liquid phase. In the
second, the energy equation considering both heat conduction and natural convection is solved to
predict the behaviour of the PCM. Different PCM materials, geometries and configurations of the
storage device are considered and tested in order to evaluate the effectiveness of the adopted
numerical codes under different working conditions. Finally, the models are validated using
experimental data obtained from tests carried out on a double tube heat exchanger with fins and
with Rubitherm® RT35 paraffin as PCM. The tests are conducted in the laboratories of the
University of Lleida (Spain) by the research group GREA Innovació Concurrent.
The second part of this work concerns the design and implementation of a test rig, specifically
built for experimental investigation of heat storage devices in the laboratory for TES technologies
of the University of Cagliari. An accurate study and selection of both the test rig layout and all the
needed equipment is carried out to perform experimental analysis.
The test bench is composed of an electrical heater, which heats the HTF up to the operating
temperature, an air cooler, which simulate the thermal demand during the discharge phase, a HTF
circulating pump, two test sections for thermal energy storage systems, and a preliminary TES
device which consists in a shell and tube heat exchanger, where the HTF flows in the tubes while
the PCM is placed in the shell side. At this stage, the thermal energy storage system, the
measuring devices and the data acquisition system are under implementation.
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Contents
Acknowledgements .......................................................................................................................... ii
Abstract ........................................................................................................................................... iii
List of figures .................................................................................................................................. vi
List of Tables ................................................................................................................................ viii
Chapter 1 Introduction .................................................................................................................. 1
1.1 Motivation and objective ................................................................................................. 1
1.2 Overview of the thesis...................................................................................................... 6
1.3 Publication ....................................................................................................................... 7
Chapter 2 Methods for thermal energy storage ............................................................................ 8
2.1 Introduction ...................................................................................................................... 8
2.2 Sensible Heat Storage .................................................................................................... 10
2.3 Latent Heat Storage ........................................................................................................ 11
2.4 Thermochemical Heat Storage ....................................................................................... 12
2.5 Comparison of TES types .............................................................................................. 14
Chapter 3 Phase Change Materials (PCM) ................................................................................. 16
3.1 Introduction .................................................................................................................... 16
3.2 Classification of PCM .................................................................................................... 17
3.2.1 Organic PCM ......................................................................................................... 18
3.2.2 Inorganic PCM ....................................................................................................... 21
3.2.3 Eutectics ................................................................................................................. 24
3.3 Performance of TES systems with PCM ........................................................................ 25
3.3.1 High-thermal conductivity material enhancers ...................................................... 27
3.3.2 Extended heat transfer surface enhancers .............................................................. 27
3.3.3 Intermediate heat transfer medium enhancers ........................................................ 28
3.3.4 Heat pipe enhancers ............................................................................................... 29
3.3.5 Multiple PCM enhancers ....................................................................................... 29
Chapter 4 Mathematical models of the PCM thermal energy storage system ............................ 31
4.1 Introduction .................................................................................................................... 31
4.2 Mathematical models ..................................................................................................... 31
4.2.1 Apparent heat capacity formulation ....................................................................... 32
4.3 First approach: 3D numerical model .............................................................................. 34
4.3.1 Material and method .............................................................................................. 34
4.3.2 Results and discussion ........................................................................................... 40
4.4 Second approach: 2D axysimmetric numerical model ................................................... 43
v
4.4.1 Introduction ............................................................................................................ 43
4.4.2 Material and method ............................................................................................... 44
4.4.3 Results and discussion ............................................................................................ 48
4.5 Validation of the 2D axysimmetric model: comparison between the two approaches ... 54
4.5.1 Material and method ............................................................................................... 54
4.5.2 Results and discussion ............................................................................................ 57
4.6 Conclusions .................................................................................................................... 63
Chapter 5 Project design and implementation of a TES test rig ................................................ 66
5.1 Introduction .................................................................................................................... 66
5.2 Design and implementation of the LHTES test rig ........................................................ 66
5.2.1 Skid ......................................................................................................................... 69
5.2.2 Air cooler ................................................................................................................ 72
5.2.3 Air Separation Unit ................................................................................................. 73
5.2.4 Thermal energy storage device ............................................................................... 73
5.2.5 LMTD method ........................................................................................................ 76
5.2.6 Design of the TES device ....................................................................................... 80
Chapter 6 Dynamic analysis of a pilot plant based on LHTES system for DSG applications at
Plataforma Solar de Almeria .......................................................................................................... 85
6.1 Introduction .................................................................................................................... 86
6.2 Material and method ....................................................................................................... 87
6.3 Conclusions .................................................................................................................... 95
Chapter 7 Conclusions and future research ................................................................................. 96
References ...................................................................................................................................... 99
vi
List of figures
Fig. 1.1 - Classification of energy storage technologies by the form of stored energy [4]. ............. 1
Fig. 1.2 - Schematic of flow battery [7] ........................................................................................... 2
Fig. 2.1- Examples of TES system configurations classified as active and passive storage systems
[15] ................................................................................................................................................... 9
Fig. 2.2- Methods of thermal energy storage ................................................................................... 9
Fig. 2.3- TES complete storage cycle. ........................................................................................... 10
Fig. 2.4- Comparison between sensible and latent heat. ................................................................ 12
Fig. 2.5- Scheme of closed (a) and open (b) sorption storage systems [21] .................................. 13
Fig. 2.6 - Sorption thermal storage methods and materials [9] ..................................................... 13
Fig. 3.1- Classification of PCM ..................................................................................................... 17
Fig. 3.2 - Classes of PCM related with melting enthalpy and melting temperature ...................... 18
Fig. 3.3 - Classification of investigated performance enhancement techniques in TES-PCM [24]26
Fig. 3.4 - Examples of enhancement techniques in TES-PCM ...................................................... 26
Fig. 3.5- Reflux heat transfer storage concept ............................................................................... 28
Fig. 3.6- Heat transfer between PCM and HTF using heat pipes [34] ........................................... 29
Fig. 3.7- Multiple PCM configuration in thermal energy storage systems .................................... 30
Fig. 4.1- Smoothed function used to evaluate Cp in apparent heat capacity formulation .............. 33
Fig. 4.2 - Geometrical configuration of TES system ..................................................................... 35
Fig. 4.3 - Mesh using for the TES simulation ................................................................................ 36
Fig. 4.4 - Profiles of PCM temperature for (a) charge phase, and (b) discharge phase ................. 40
Fig. 4.5 - Profiles of PCM temperature and solid-liquid interface evolution in the charge phase . 41
Fig. 4.6 - Profiles of PCM temperature and solid-liquid interface evolution in the discharge phase
....................................................................................................................................................... 42
Fig. 4.7 - Geometrical configuration of the three TES systems. .................................................... 45
Fig. 4.8 - PCM temperature profile for charge (a) and discharge (b) processes. ........................... 49
Fig. 4.9 - Phase evolution of PCM during charge and discharge process ...................................... 50
Fig. 4.10 - Melting Fraction for charge (a) and discharge (b) processes. ...................................... 51
Fig. 4.11 - Number of fins effect to the melting time .................................................................... 53
Fig. 4.12 - Double tube heat exchanger with fins (a), geometric configuration of TES system
implemented in COMSOL Multiphysics (b). ................................................................................ 54
Fig. 4.13 - Diagram of experimental set-up ................................................................................... 55
Fig. 4.14 - PCM temperature profile for charge (a) and discharge (b) processes. ......................... 58
Fig. 4.15 - Melting process for experiment 1 (a) and experiment 2 (b) during charge process ..... 59
Fig. 4.16 - Melting fraction for both approaches during discharge process ................................... 59
vii
Fig. 4.17 - Phase evolution of PCM for both experiments and for both approaches during charge
and discharge process ..................................................................................................................... 61
Fig. 4.18 - Convection cells within PCM during melting process at 800s for experiment 1 .......... 62
Fig. 4.19 - Free triangular mesh used for first approach (a) and second approach (b) ................... 63
Fig. 5.1 - Test rig layout ................................................................................................................. 67
Fig. 5.2 - Valves system to modify the direction of the HTF at the inlet of the TES ..................... 68
Fig. 5.3 - Two different modes concerning the HTF direction at TES inlet ................................... 69
Fig. 5.4 - Skid of the test rig ........................................................................................................... 70
Fig. 5.5 - Pump characteristic and system curves ........................................................................... 71
Fig. 5.6 - Air cooler placed outside the laboratory ......................................................................... 72
Fig. 5.7 - Scheme of air cooler ....................................................................................................... 73
Fig. 5.9 - TES layout (a) and tube bundle scheme (b) .................................................................... 75
Fig. 5.10 - Fluid temperature variation in heat exchanger when occurs phase transition during
charge (a) and discharge (b) processes. .......................................................................................... 76
Fig. 5.11 - Tube sheet layout [74] .................................................................................................. 83
Fig. 6.1 - Layout of the hybrid solar thermal power plant (REELCOOP project) ......................... 87
Fig. 6.2 - Test facility layout during charge phase ......................................................................... 88
Fig. 6.3 - Test facility layout during discharge phase .................................................................... 88
Fig. 6.4 - Pump characteristic curve head-flow .............................................................................. 89
Fig. 6.5 - Circulating pump model ................................................................................................. 90
Fig. 6.6 - Schematic picture of a boiler system [99] ....................................................................... 91
Fig. 6.7 - Model of the boiler implemented in Simulink ................................................................ 93
Fig. 6.8 - Schematic picture of the mixer ....................................................................................... 94
Fig. 6.9 - Mixer model implemented in Simulink .......................................................................... 95
viii
List of Tables Table 1.1- A summary of mechanical energy storage technologies [5].Errore. Il segnalibro non è
definito.
Table 1.2- Summary of battery storage technologies [5]. ...... Errore. Il segnalibro non è definito.
Table 1.3- Heat demand for different industrial processes by sectors and temperature ranges
............................................................................................... Errore. Il segnalibro non è definito.
Table 2.1 - Typical materials used in sensible heat storage systems ............................................. 10
Table 2.2 - Properties of materials used in CSP plants .................................................................. 11
Table 2.3 - Comparison of different thermal energy storage systems ........................................... 14
Table 3.1 - Example of paraffins that have been investigated as PCM [7] ..... Errore. Il segnalibro
non è definito.
Table 3.2 - Examples of fatty acids that have been investigated as PCM [7] . Errore. Il segnalibro
non è definito.
Table 3.3 - Examples of sugar alcohols that have been investigated as PCM [7] ......................... 20
Table 3.4 - Examples of glycols that have been investigated as PCM [7] ...... Errore. Il segnalibro
non è definito.
Table 3.5 - Examples of salt hydrates that have been investigated as PCM [7] ................ Errore. Il
segnalibro non è definito.
Table 3.6 - Examples of salt that have been investigated as PCM [7] .. Errore. Il segnalibro non è
definito.
Table 3.7 - Examples of metallics that have been investigated as PCM [10] . Errore. Il segnalibro
non è definito.
Table 3.8 - Examples of metallics that have been investigated as PCM [3] ... Errore. Il segnalibro
non è definito.
Table 4.1 - Properties of Hydroquinone ......................................................................................... 35
Table 4.2 - Geometrical characteristics and operating parameters of storage system ................... 36
Table 4.3 - Properties of D-Mannitol. ............................................................................................ 44
Table 4.4 - Geometrical characteristics of the storage system ...................................................... 46
Table 4.5 - Number of fins and melting times for five different cases analyzed ........................... 52
Table 4.6 - Geometrical characteristics of storage system ............................................................. 54
Table 4.7 - Properties of Rubitherm RT35 .................................................................................... 55
Table 4.8- Summary of charging and discharging experiments carried out. ................................. 56
Table 4.9. - Value of Rans model costants [63] [64] ..................................................................... 57
Table 4.9 - Summary of the model simulations to compare the two approaches studied. ............. 62
Table 5.1 - Operating parameters of the test rig ............................................................................ 66
Table 5.2 - Geometrical characteristics and design operating parameters of PCM-TES device ... 74
Table 5.3 - Operating parameters of PCM-TES device using D-Mannitol .................................... 74
Table 5.3 - Representative fouling factors in heat exchangers ...................................................... 80
ix
Table 5.4 - Typical overall heat transfer coefficient for shell and tube heat exchangers ............... 82
Table 6.1 - Operational solar thermal facilities with thermal energy storage systems. .................. 86
Table 6.2- Cohen-Coon Formulas .................................................................................................. 92
Chapter 1 1
Chapter 1
Introduction
1.1 Motivation and objective
In the last decades, the increase in energy demand, together with a growing awareness of the
limitation of emissions of greenhouse gases and pollutants, resulted in a significant impulse to the
development of technologies aimed at energy saving and at the production of energy from
renewable sources. The Intergovernmental Panel on Climate Change (IPCC) report [1] shows that
humankind plays a fundamental role on climate change owing to CO2 emissions from energy
consumption, and that a significant reduction in CO2 emissions is necessary within next decades.
The use of renewable energy sources and increased energy efficiency are the main strategies to
reduce the dependency of fossil fuels and CO2 emissions. However, as it is known, renewable
energy sources such as solar and wind energy in particular, are not only characterized by
discontinuous availability but are also affected by random variations due to local weather
conditions.
In this scenario, the availability of energy storage would be essential allowing a large number of
solutions and combination of different technologies from already existing power generation
systems [2]. Energy storage not only reduces the mismatch between supply and demand but also
improves the performance and reliability of energy systems and plays an important role in
conserving the energy. The energy storage could also be used to offset the temporary decreases of
production from conventional energy sources, ensuring the expected level of demand, allowing a
reduction of the peak and an improvement of the efficiency of the plant, with the result of fuel
savings [3]. The different forms of energy that can be stored include mechanical, electrical and
thermal energy (Fig. 1.1).
Fig. 1.1 - Classification of energy storage technologies by the form of stored energy [4].
2 Chapter 1
The most common mechanical storage systems are pumped hydroelectric storage (PHS) power
plants, compressed air energy storage (CAES) and flywheel energy storage (FES) as reported in
Table 1.1 [5]. The PHS and CAES technologies can be used for large-scale utility energy storage
while flywheels are more suitable for intermediate storage [6].
Table 1.1 - A summary of mechanical energy storage technologies [5].
Technology Advantages Disadvantages
PHS Mature technology, high energy and
power capacity, least cost for large-
scale power, long life.
Requires special sites for upper and lower
water reservoirs, high capital cost, long
construction time
CAES Mature technology, high energy and
power capacity, least cost for large-
scale power, long life.
Requires special geological sites, high
capital cost, long construction time, need
gas fuel input
FES High power density, flat voltage
profile, better life cycle than batteries
Low energy density, short term power,
large standby losses high initial cost
Electrical Energy Storage (EES) refers to a process of converting electrical energy from a power
network into a form that can be stored for converting back to electrical energy when needed. The
use of batteries is an option for storing the electrical energy. Potential applications of batteries are
utilization of off-peak power, load levelling, and storage of electrical energy generated by wind
turbine or photovoltaic plants. The most common type of storage batteries is the lead acid and Ni–
Cd [6], but for medium and large scale stationary applications new technologies are available,
such as nickel–metal hydride (Ni-MH) and lithium-ion (Li-ion) batteries. The flow batteries, as
shown in Fig. [7], are a form of a battery in which the electrolyte contains one or more dissolved
electro-active species flowing through a power cell/reactor in which the chemical energy is
converted to electricity.
Fig. 1.2 - Schematic of flow battery [7]
Chapter 1 3
Additional electrolyte is stored externally, generally in tanks, and is usually pumped through the
reactor cells. The reaction is reversible allowing the battery to be charged, discharged and
recharged [7]. The most common type of flow battery is zinc–bromine (ZnBr). A summary of
battery storage technologies is shown in Table 1.2 [5].
Table 1.2 - Summary of battery storage technologies [5].
Technology Advantages Disadvantages
NaS High energy and power density, relatively
matured, high efficiency and excellent life
cycle
High initial cost, safety concerns
ZnBr High energy and power density, flat
voltage profile
Relatively new and untested
Regenerative zinc
air Li ion
High energy and power density Relatively new and untested
Li ion High energy and power density, long life,
high efficiency
High initial cost, requires
sophisticated management
(balancing and charge control
electronics)
VRB Relatively high energy and power density,
easily upgradeable
Not yet proven for cycle life or
maintenance cost, relatively
expensive
Lithium metal
polymer batteries
High energy and power density, relatively
tolerant to temperature extremes
Requires balancing and charge
control electronics, high initial
cost, relatively untested
Vented Ni-Cg Mature and well known, high efficiency
high energy and power density, better
lifecycle than lead acid, relatively tolerant
to temperature extremes
Float effetc makes capacity testing
difficult, more expensive than lead
acid, toxic components (cadmium),
low cell voltage
NiMH Less toxic than Ni-Cd, mature technology,
high energy and power density, better
cycle life than lead acid
Float effect makes capacity testing
difficult, more expensive than lead
acid, low cell voltage, intolerant of
temperature extremes
Valve regulated Pb
acid
Low maintenance, low initial cost Low life, intolerant of temperature
extremes
Vented Pb acid mature and well known, low cost, high
reliability and efficiency
poor low temperature performance,
high maintenance cost, low energy
density and cycle life, can't handle
temperature extremes
Thermal energy storage can be based on a change in internal energy of a material as sensible heat,
latent heat, thermochemical or combination of these. In the first case, the storage is based on the
temperature change of a liquid or a solid material. In the second case, thermal energy is stored as
latent heat during a phase transition. The third type uses an endothermic chemical reaction, where
the energy associated with a reversible reaction is required for the dissociation of the chemicals
[8].
The main objective of this PhD research project is the modelling, the design and the analysis of
TES devices based on latent heat storage for renewable energy and other non programmable
4 Chapter 1
energy sources, industrial processes and heat and power generation for intermediate temperature
applications (150-250 °C).
Real applications of Latent Heat Thermal Energy Storage (LHTES) systems for the temperature
range chosen are typically used in solar technologies associated with Organic Rankine Cycle
(ORC) (e.g. REELCOOP EU/FP7 project), or in general in concentrating small-medium scale
solar power (CSP). In the same temperature range, PCM materials are also used in various types
of industrial applications such as in solar cooling systems with absorption chiller [9], related to
fuel cell PAFC or heat recovery in metal hydrides hydrogen storage systems. Other application
areas are in the food, beverage, transport equipment, textile, machinery, pulp and paper industries
and drying of agricultural products, where roughly 60% of the heating needs is required
temperatures below 250°C [10] [11]. Temperature range for reported industrial applications are
listed in Table 1.3.
Table 1.3 - Heat demand for different industrial processes by sectors and temperature ranges
Industry Process Temperature [°C]
Dairy Pressurization 60-80
Sterilization 100-120
Drying 120-180
Concentrates 60-80
Boiler feed water 60-90
Tinned Food Sterilization 110-120
Pasteurization 60-80
Cooking 60-90
Bleaching 60-90
Textile Bleaching, Dyeing 60-90
Drying, Degreasing 100-120
Dyeing 70-90
Fixing 160-180
Pressing 80-100
Paper Cooking, Drying 60-80
Boiler feed water 60-90
Bleaching 130-150
Chemical Soap 200-250
Synthetic rubber 150-200
Processing heat 120-180
Pre-heating water 60-90
Meat Wash, Sterilization, Cleaning 60-90
Cooking 90-100
Tinned food Sterilization 60-70
Cooking 90-100
Beverages Washing, Sterilization 60-80
Pasteurization 60-70
Flours & by-prod. Sterilization 60-80
Timber by-products Thermodiffusion beams 80-100
Drying 60-100
Chapter 1 5
Pre-heating water 60-90
Preparation pulp 120-170
Automobile Painting 160-220
Drying 60-100
Cooking 60-90
Bricks and blocks Curing 60-140
Plaster Calcinating 140-160
Curing plasterboard 230-250
Glass Sheets 100-150
Drying fibre-glass 110-130
Plastics Preparation 120-140
Distillation 140-150
Saparation 200-220
Extension 140-160
Drying 180-200
Blending 120-140 Source: GESA Research Group, 1988
Suitable materials for accomplishing this task are Phase Change Materials (PCM). A Phase
Change Material is a material that change its phase at a certain temperature storing or releasing
large amount of energy called latent heat. The latent heat change is usually much higher than the
sensible heat change for a given medium, which is related to its specific heat. Solar energy
applications require large TES capacities in order to cover the lack of daytime radiation for
meteorological reasons or simply overnight. This capacity is commonly achieved by sensible heat
storage systems. A valid alternative is offered by latent heat storage systems, where thermal
energy is stored as latent heat in substances undergoing a phase transition, for example, the heat
of fusion in the solid–liquid transition. The main advantages of LHTES systems are high thermal
energy storage capacities per unit mass compared to those of sensible heat systems, and a small
temperature range of operation since the heat interaction occurs at approximately constant
temperature.
This work is based on two parts: the first part is the study and the analysis of numerical models in
order to simulate the transient behaviour of the PCM-TES, to predict the energy balance in space
and time and the TES overall performances. The second part concerns the design and the
implementation of a test rig specifically built for experimental investigation of heat storage
devices. The test rig, implemented in the laboratory for TES technologies of the Department of
Mechanical, Chemical and Materials Engineering (DIMCM) of the University of Cagliari, can be
used not only to validate all the developed numerical models, but also to carry out a considerable
research activity in the field of thermal energy storage based on modeling, control and testing of
innovative TES systems for industrial applications. Main objectives of this research activity will
be the performance evaluation of PCM-TES prototypes with respect to energy stored/released,
time and efficiency during repeated cycles of charge/discharge, the analysis on different materials,
geometries and heat transfer enhancement techniques in order to optimize the entire process.
The numerical models implemented in COMSOL Multiphysics are used to simulate latent heat
storage systems with different geometries and different working materials. The numerical analysis
is based on development of three and two-axisymmetric dimensional models, where energy
6 Chapter 1
equation is used in accordance with the apparent heat capacity formulation to solve and model the
phase transition of a PCM material chosen.
Finally, because of the test rig of the DIMCM has not yet been completed, the numerical models
proposed have been validated by comparison with experimental results carried out with the
experimental facilities of the GREA Innovació Concurrent situated in the University of Lleida
(Spain). The result demonstrates its validity and feasibility to simulate real application in thermal
energy storage with PCM.
1.2 Overview of the thesis
This Thesis is structured in six main chapters and a concluding chapter subdivided in paragraphs
for each topic.
A brief description of each chapter is given in the following:
Chapter 2: A general overview of the different methods of thermal energy storage is
presented with respect to their characteristics, focusing the attention to the latent heat
thermal storage systems. Furthermore, a comparison between these different methods is
also presented, in order to evaluate the advantages and disadvantages of the latent heat
storage with respect to the other technologies.
Chapter 3: A summary of the different classes of PCM materials is reported with respect
to their most important properties, advantages and disadvantages. Furthermore a
description of the basic requirements to use them as phase change material is discussed.
In the last part of this chapter, various method to increase thermal conductivity of PCM
are also discussed.
Chapter 4: The numerical models used to simulate the latent heat thermal energy storage
systems are introduced. A description of equations, geometries, configurations and
materials used is presented. Different models are investigated using two approaches to
model the PCM during transition process: in the first heat transfer only by conduction is
considered, in the second heat transfer by conduction and natural convection are
considered. Finally, the numerical results are compared with an experimental test in order
to validate the accuracy of the models.
Chapter 5: The design of a test rig to investigate thermal energy storage systems within
the laboratory of the Department of Mechanical, Chemical and Material of the University
of Cagliari is presented. A description of the facility components and of the latent heat
storage device is also reported.
Chapter 6: The study of a real application of latent heat thermal energy storage system in
the research center Plataforma Solar de Almeria (Spain) are reported. Description of the
pilot plant equipments and operation mode is reported. A simplified numerical model to
Chapter 1 7
simulate the dynamic behaviour of the entire system during the charge and discharge
process is presented.
Chapter 7: The main conclusions and the possible future development of this research
are discussed.
1.3 Publication
Some of the topics discussed in this Thesis have been already published in international journal,
and presented at national and international conferences.
International Journal Papers:
1. Arena S., Cau G., Palomba C., CFD Simulation of Melting and Solidification of PCM in
Thermal Energy Storage Systems of Different Geometry, Journal of Physics: Conference
Series 655.
2. Migliari L., Arena S., Thermal Energy Losses During Night, Warm-Up and Full-
Operation Periods of a CSP Solar Field Using Thermal Oil, Energy Procedia 82 (1002-
1008) doi:10.1016/j.egypro.2015.11.858
National and International Conferences:
1. Arena S., Cau G., Palomba C., Development and Implementation of a 3D Numerical
Code for Designing and Predicting Performances of PCM Thermal Energy Storage
Systems, Eurotherm Seminar n°99 - Advances in Thermal Energy Storage, Lleida, Spain
2014.
2. Arena S., Casti E., Cascetta M., Serra F., Cau G., Performance Analysis of Thermal
Energy Storage (TES) Systems based on Sensible and Latent Heat for Concentrated Solar
Power (CSP) Applications, Ricerca in Vetrina, Alghero, Italy 2015.
8 Chapter 2
Chapter 2
Methods for thermal energy storage
2.1 Introduction
Thermal energy storage (TES) systems allow the storage of heat or cold for later use. The main
use of TES are in all the applications where exist a mismatch between energy production and use
like in the case of renewable energies which are by nature intermittent and whose availability is
further reduced by weather perturbation. Solar energy is available only during the day, and hence,
its application requires an efficient thermal energy storage so that the excess heat collected during
sunshine hours can be stored for later use during the night. Similar problems occur in heat
recovery systems and industrial processes where the waste heat availability and utilization periods
are different, requiring some thermal energy storage. Also, electrical energy consumption varies
significantly during the day and night, especially in extremely cold and hot climate countries
where the major part of the variation is due to domestic space heating and air conditioning. Such
variation leads to an off-peak period, usually after midnight until early morning. Accordingly,
power stations have to be designed for capacities sufficient to fulfil the peak load. Otherwise, very
efficient power distribution would be required. Better power generation management can be
carried out if some of the peak load could be shifted to the off-peak load period, which can be
achieved by energy storage. Hence, the successful application of load shifting depends to a large
extent on the method of energy storage adopted [12]. Generally, it is possible to divide thermal
storage systems in active and passive systems. An active storage system contains a mechanically
assisted component for enabling the heat transfer between the system and the heat source.
Therefore, this systems are characterized by forced convection heat transfer into the storage
material that circulates through a heat exchanger, a solar receiver or a steam generator. In a
passive storage system, the heat transfer between the system and the heat source occurs by means
of natural convection or buoyancy forces (due to density gradient) without the assistance of any
external devices [13]. Active storage systems can be divided into direct and indirect systems. In
the direct systems, the heat transfer fluid (HTF) is used also as storage medium, while in the
indirect systems, a second medium is used for storing the heat [14]. Figure 2.1 reports some TES
system configurations classified as active and passive storage systems.
Chapter 2 9
Fig. 2.1- Examples of TES system configurations classified as active and passive storage
systems [15]
Thermal energy can basically be classified according to the way heat is stored: as sensible heat,
latent heat or chemical energy (Fig. 2.2).
Fig. 2.2 - Methods of thermal energy storage
Each of these types presents a sequential process of charge, storage and discharge giving a
complete storage cycle as reported in Figure 2.3.
10 Chapter 2
Fig. 2.3 - TES complete storage cycle.
2.2 Sensible Heat Storage
In sensible heat storage systems (SHSS), thermal energy is stored by raising the temperature of a
solid or liquid media. Sensible heat storage is by far the common method for heat storage, for
example, hot water heat storage is used for domestic heating and domestic hot water in every
household. The amount of energy stored is given by the relation:
𝑄 = ∫ 𝑚𝐶𝑝𝑑𝑇 = 𝑚𝐶𝑝̅̅ ̅(𝑇𝑓 − 𝑇𝑖)𝑇𝑓
𝑇𝑖
(2.1)
where 𝑄 is the amount of heat stored in the material, 𝑚 is the mass of storage material, 𝐶𝑝̅̅ ̅ is the
mean specific heat of the material evaluated in the operative temperature range and 𝑇𝑖 and 𝑇𝑓 are
the initial and final temperature of the process respectively.
A large number of materials are available in any required temperature range therefore, the storage
material is usually selected according to its heat capacity and the available space for storage.
Gases have very low volumetric heat capacity and therefore are not used for sensible heat or cold
storage. Table 2.1 reports some common materials used in SHSS [16].
Table 2.1 - Typical materials used in sensible heat storage systems
Material Density
[kg/m3]
Specific heat
[J/kg∙K]
Volumetric thermal capacity
[MJ/m3∙K]
Clay 1458 879 1.28
Brick 1800 837 1.51
Sandstone 2200 712 1.57
Wood 700 2390 1.67
Concrete 2000 880 1.76
Glass 2710 837 2.27
Aluminium 2710 896 2.43
Chapter 2 11
Iron 7900 452 3.57
Steel 7840 465 3.68
Gravelly earth 2050 1840 3.77
Magnetite 5177 752 3.89
Water 988 4182 4.17
In Table 2.2 are presented some materials mostly used in CSP storage applications [17].
Table 2.2 - Properties of materials used in CSP plants
Material Density
[kg/m3]
Specific heat
[J/kg∙K]
Thermal conductivity
[W/mK]
Cost
[€/kg]
Cost
[€/kWh]
ΔT=100 °C
Molten Salt 900-2600 1500 0.15-2 0.63 14
Colafite 3120 800-1034 1.4-2.1 0.01 0.4
Castable ceramics 3500 866 1.35 4.5 188
High temperature
concrete
2750 916 1 0.08 3
Water appears to be the best available liquid SHSS because it is cheap and has a high specific heat
and volumetric thermal capacity. However above 100 °C, materials such as oils, molten salts and
liquid metals are preferred since water should be pressurized. For air heating applications rock or
metal bed type storage materials are used [6].
2.3 Latent Heat Storage
Latent heat storage is based on the heat absorption and release when a storage material undergoes
a phase change. PCM can store 5–14 times more heat per unit volume than sensible heat storage
materials such as water, masonry, or rock. Phase change can occur in different forms: solid–solid,
solid–liquid, solid–gas, liquid–gas. Solid–liquid transitions are an economically attractive option
for use in thermal energy storage systems. In fact these transformations have comparatively
smaller latent heat than liquid–gas, but involve only a small change (of about 10% or less) in
volume. The storage capacity of the LHTES system with a solid-liquid process is given by:
𝑄 = 𝑚 [∫ 𝐶𝑝,𝑠𝑑𝑇 + 𝜆 +∫ 𝐶𝑝,𝑙𝑑𝑇𝑇𝑓
𝑇𝑚
𝑇𝑚
𝑇𝑖
] (2.2)
The first term of the second member is the sensible heat of the solid phase, 𝜆 represents the
specific latent heat and, finally, the third term is the sensible heat of the liquid phase. In the
Equation 2.2, 𝐶𝑝,𝑠 and 𝐶𝑝,𝑙 are specific heat of solid and liquid phase respectively and 𝑇𝑚 is the
melting temperature of the material.
12 Chapter 2
With respect to other techniques, latent heat thermal energy storage is particularly attractive due
to both its ability to provide high-energy storage density and its characteristic to store heat at
constant temperature corresponding to the phase-transition temperature (Fig 2.4).
Fig. 2.4- Comparison between sensible and latent heat.
A large number of PCM are known to melt with a heat of fusion in any range of interest.
However, for their employment these materials must exhibit certain desirable thermodynamic,
kinetic and chemical properties. In Chapter 3 a list of different classes of PCM materials is
reported with respect to their important properties, advantages and disadvantages.
2.4 Thermochemical Heat Storage
Thermochemical TES systems use an endothermic chemical reaction, where the energy associated
with a reversible reaction is required for the dissociation of the chemicals [8]. In this case, the
heat stored is given by Equation 2.3:
𝑄 = 𝑎𝑟𝑚∆ℎ𝑟 (2.3)
where 𝑎𝑟 is the extent of conversion, 𝑚 is the amount of storage material and ∆ℎ𝑟 is the
endothermic heat of reaction. Thermochemical materials have higher energy densities relative to
PCMs and sensible storage media [14]. Because of higher energy density, thermochemical TES
systems can provide more compact energy storage relative to latent and sensible TES. This
attribute is particularly beneficial where space for the TES is limited or valuable [18]. Drawbacks
include complexity and high cost [19]. Thermochemical energy is divided in two different
systems: chemical reactions and sorption systems. In chemical reactions storage systems, high
Chapter 2 13
energy storage density and reversibility is required to the materials [14]. Usually TES based on
chemical reaction have better energy storage performance efficiency than sensible and latent heat
storage systems. These systems are used as storage at high temperature (more than 400 °C) and
the main reaction used are the carbonation reaction, ammonia decomposition, metal oxidation
reactions and sulfur cycles [20].
In sorption systems, heat is stored by separation of substances. To recover heat, the substances are
recombined. This technologies are divided into closed and open sorption storage systems as
reported in figure 2. [21].
(a) (b)
Fig. 2.5- Scheme of closed (a) and open (b) sorption storage systems [21]
The first configuration takes the sorbate from the ambient, while in the second, the sorbate
remains within the system (not only water can be used but also other liquids such as ammonia or
methanol), and only the evaporation heat is taken from the ambient. The most common sorbents
are reported in figure 2.4.
Fig. 2.6 - Sorption thermal storage methods and materials [9]
14 Chapter 2
2.5 Comparison of TES types
A quantitatively comparison of the different thermal energy storage technologies is reported in
table 2.3, considering a range of relevant performance parameters and factors. It is evident that the
various technologies have different operating characteristics, advantages and disadvantages. For
different applications, different TES can be the most suitable choice.
Table 2.3 - Comparison of different thermal energy storage systems
Sensible TES Latent TES Thermochemical TES
Temperature range Up to:
50 °C (Aquifers and
ground storage)
110 °C (Water tanks)
300 °C (Sand-rock-
mineral oil)
400 °C (Siliconic oil)
400 °C (Concrete)
500 °C (NaCl, solid)
700 °C (Cast steel)
1200 °C (Magnesia fire
bricks)
-100 ÷0 °C (Water-salt
solutions)
-50÷0 °C (Clathrates)
-20÷100 °C (Paraffins)
-20÷80 °C (Salt hydrates)
20÷450 °C (Sugar
alcohols)
120÷300 °C (Nitrates)
150÷400 °C (Hydroxides)
350÷750 °C (Chlorides)
400÷800 °C (Carbonates)
700÷900 °C (Fluorides)
180 °C (Iron carbonate)
200÷300 °C (Metal
hydrides)
250÷400 °C
(Magnesium oxide)
400÷500 °C (Ammonia)
800÷900 °C (Calcium
carbonate)
500÷1000 °C
(Methane/water)
2000÷2500 °C (Metal
oxides Zn and Fe)
Energy density
Volumetric density
Gravimetric density
Small ~ 50 kWh/m^3 of
material
Small ~ 0.02-0.03
kWh/m^3 of material
Medium ~ 100 kWh/m^3
of material
Medium ~ 0.05-1
kWh/m^3 of material
High ~ 500 kWh/m^3
of material
High ~ 0.5-1 kWh/m^3
of material
Storage period Limited (thermal losses) Limited (thermal losses) Theoretically unlimited
Lifetime Long Often limited due to
storage material cycling
Depends on reactant
degradation and side
reactions
Technology status Industrial scale Pilot scale Laboratory scale
Advantages Low cost
Reliable
Simple application with
available materials
Medium storage density
Small volumes
Short distance transport
possibility
High storage density
Low heat losses
(storage at ambient
temperature)
Long distance transport
possibility
High compact energy
storage
Disadvantages Significant heat loss over Low heat conductivity High capital costs
Chapter 2 15
time (depending on level
of insulation)
Large volume needed
Corrosivity of materials
Significant heat loss
(depending on level of
insulation)
Technically complex
16 Chapter 3
Chapter 3
Phase Change Materials (PCM)
3.1 Introduction
Thermal energy storage systems based on phase change materials are considered to be an efficient
alternative to sensible thermal storage systems. Furthermore, these systems have high energy
density compared to sensible heat storage systems. As said before PCM include the solid-solid,
the solid-liquid, the solid-gas and the liquid-gas type.
In solid–solid transitions, heat is stored during the change from one crystalline to another. These
transitions generally have small latent heat and small volume changes than solid–liquid
transitions. Solid–solid PCM offer the advantages of less strict container requirements and greater
design flexibility. Solid–gas and liquid–gas transition have higher latent heatof vaporization but
their large change in volume on phase transition are associated with the containment problems
and restricts their application in TES. Solid–liquid transformations have comparatively smaller
latent heat than liquid–gas, but involve only a small volume change (of order of 10% or less). For
this reasons, solid–liquid transitions is considered the most interesting and economically attractive
option to be applied in thermal energy storage systems.
The PCM to be used in the design of thermal-storage systems require desirable thermo-physical,
kinetics chemical and economical properties [6][16][22] thus, generally, a material is not able to
achieve all these requirements.
a) Thermal requirements
Suitable phase-transition temperature to assure storage and release of heat at the
correct temperature for each application.
High latent heat of transition to achieve a large storage density in order to minimize
the physical size of the heat store.
High thermal conductivity to assure storage and release of latent heat in a short time
during charging and discharging operation.
b) Physical requirements
High density to minimize the size of storage container.
Small volume change to reduce the containment problem.
Low vapor pressure to reduce the containment problem.
Favorable phase equilibrium to assure the stability of the storage capacity during
cycles.
Chapter 3 17
c) Kinetic requirements
No subcooling to guarantee that melting and solidification take place at correct
temperature transition range. The subcooling happens when a PCM do not solidify
immediately upon cooling below the melting temperature; in this case the
crystallization starts only after a temperature well below the melting temperature is
reached. The effect of subcooling involves the reduction of the temperature below the
phase change temperature to start crystallization and to release the latent heat stored
in the material. If nucleation does not happen at all, the latent heat is not released at
all and the material only stores sensible heat [16].
Good crystallization rate.
d) Chemical requirements
Chemical stability to avoid degradation after a large number of cycles.
Compatibility with other materials to avoid problems of corrosion with container.
Non toxic, non flammable and non explosive behaviour for safety and environmental
impact.
e) Economics requirements
Low price to be competitive with other thermal storage technologies.
Good recyclability for environmental and economic reasons.
3.2 Classification of PCM
PCM materials can be divided in three groups as reported in figure 3.1.
Fig. 3.1- Classification of PCM
18 Chapter 3
Figure 3.2 shows common classes of PCM related with the melting enthalpy and the melting
temperature [16].
Fig. 3.2 - Classes of PCM related with melting enthalpy and melting temperature[16]
A short overview on properties, advantages and disadvantages of the different classes of PCM
materials is given below.
3.2.1 Organic PCM
Organic materials are divided into two groups: paraffin and non-paraffins.
Paraffins
Paraffin wax is the most common organic PCM and consists of a mixture of mostly straight chain
n-alkanes CH3-(CH2)-CH3. Generally the higher the average length of the hydrocarbon chain, the
higher the latent heat of fusion and the melting temperature. Paraffins are safe, reliable, quite
cheap and non-corrosive; others advantages are chemical stability, absence of segregation and
sub-cooling, good nucleating and constant thermo-physical properties. However, this material
shows some disadvantages such as: low thermal conductivity, high temperature transition range,
non compatible with plastic container, high volume change during solid-liquid transition and
often is flammable. Table 3.1 reports examples of paraffins used as PCM.
Chapter 3 19
Table 3.1 - Example of paraffins that have been investigated as PCM [7]
Material Melting
temperature [°C]
Melting
enthalpy [kJ/kg]
Thermal conductivity
[W/m∙K]
Density
[kg/m3]
n-Tetradecane
C14H30
6 230 -
0.21 (solid)
760 (liquid, 20°C)
-
n-Pentadecane
C15H32
10 212 -
-
770 (liquid, 20°C)
-
n-Hexadecane
C16H34
18 210,238 -
0.21 (solid)
760 (liquid, 20°C)
-
n-Heptadecane
C17H36
19 240 -
-
776 (liquid, 20°C)
-
n-Octadecane
C18H38
28 200, 245 0.148 (liquid, 40°C)
0.358 (solid, 25°C)
774 (liquid, 70°C)
814 (solid, 20°C)
n-Eicosane
C20H42
38 283 -
-
779
-
n-Triacontane
C30H62
66 - -
-
775
-
n-
Tetracontane
C40H82
82 - -
-
-
-
n-
Pentacontane
C50H102
95 - -
-
779
-
Polyethylene
CnH2n+2 n up
to 10000
110 200 -
-
-
870-940 (solid, 20 °C)
Non-Paraffins
The non-paraffin materials are fatty acids, esters, glycols and alcohols and represent the largest
category of organic PCM. These materials are flammable and should not be exposed to
excessively high temperature, flames or oxidizing agents. Fatty acids have high heat of fusion
values comparable to that of paraffin's and also present good cycle stability and no subcooling.
The disadvantages are corrosivity, toxicity, instability at high temperature and the cost (2-2.5
times than paraffins). Sugar alcohols have melting temperatures in range between 90°C to 200 °C,
present high specific melting enthalpies per unit volume but also subcooling. Some non-paraffins
are reported in Table 3.2 (fatty acids), in Table 3.3 (sugar alcohol) and in Table 3.4 (glycols).
20 Chapter 3
Table 3.2 - Examples of fatty acids that have been investigated as PCM [7]
Material Melting
temperature [°C]
Melting
enthalpy [kJ/kg]
Thermal
conductivity
[W/m∙K]
Density
[kg/m3]
Caprylic acid
CH3(CH2)6COOH
16 149 0.149 (liquid, 38°C)
-
901 (liquid, 30°C)
981 (solid, 13°C)
Capric acid
CH3(CH2)8COOH
32 153 0.149 (liquid, 40°C)
-
886 (liquid, 40°C)
1004 (solid, 24°C)
Lauric acid
CH3(CH2)10COOH
42-44 178 0.147 (liquid, 50°C) 870 (liquid, 50°C)
1007 (solid, 24°C)
Myristic acid
CH3(CH2)12COOH
58 186,204 -
0.17 (solid)
861 (liquid, 55°C)
990 (solid, 24°C)
Palmitic acid
CH3(CH2)14COOH
61,64 185,203 -
-
850 (liquid, 65°C)
989 (solid, 24°C)
Table 3.3 - Examples of sugar alcohols that have been investigated as PCM [7]
Material Melting
temperature [°C]
Melting enthalpy
[kJ/kg]
Thermal conductivity
[W/m∙K]
Density
[kg/m3]
Xylitol
C5H7(OH)5
94 263 -
-
-
1500 (solid, 20°C)
D-Sorbitol
C6H8(OH)6
97 185 -
-
-
1520 (solid, 20 °C)
Erythritol
C4H6(OH)4
120 340 0.326 (liquid, 140 °C)
0.733 (solid, 20°C)
1300 (liquid, 140°C)
1480 (solid, 20 °C)
D-Mannitol
C6H8(OH)6
167 316 -
-
-
1520 (solid, 20°C)
Galactitol
C6H8(OH)6
188 351 -
-
-
1520 (solid, 20 °C)
Table 3.4 - Examples of glycols that have been investigated as PCM [7]
Material Melting
temperature
[°C]
Melting
enthalpy [kJ/kg]
Thermal conductivity
[W/m∙K]
Density
[kg/m3]
Diethylene
glycol C4H10O3
-10 to -7 - -
-
1120 (liquid, 20°C)
-
Chapter 3 21
Triethylene
glycol C6H14O4
-7 - -
-
1120 (liquid, 20°C)
-
PEG400 8 100 0.19 (liquid, 38°C) 1125 (liquid, 25°C)
1228 (solid, 3°C)
PEG600 17-22 127 0.19 (liquid, 38°C)
-
1126 (liquid, 25°C)
1232 (solid, 4°C)
PEG1000 35-40 - -
-
-
-
PEG3000 52-56 - -
-
-
-
PEG6000 55-60, 66 190 -
-
1085 (liquid, 70°C)
1212 (solid, 25°C)
PEG10000 55-60 - -
-
-
-
3.2.2 Inorganic PCM
Inorganic materials used as PCM are divided into salt hydrate and metallics and cover a wide
temperature range (Fig. 3.2). Compared to organic PCM, inorganic materials usually have similar
melting enthalpies per unit mass, but higher ones per unit volume due to their high density.
Salt Hydrates
Salt hydrates consist of a water and salt in a discrete mixing ratio. The solid–liquid transformation
of salt hydrates is, in fact, a dehydration of hydration of the salt, although this process resembles
melting or freezing thermodynamically. Salt hydrates have been widely studied for their use in
thermal energy storage systems. There are three different kinds of melting behaviour: congruent
melting (when the anhydrous salt is completely soluble in water of hydration), in-congruent
melting (when the salt is not completely soluble in water) and semi-congruent melting (when the
liquid and solid phase are in equilibrium during phase transition). The advantages of this materials
are: high latent heat of fusion per unit volume, relatively high thermal conductivity (almost
double of the paraffins), small volume changes during melting process, non corrosive, compatible
with plastics, only slightly toxic and quite cheap. The main drawback is the in-congruent melting.
As n moles of water of hydration are not sufficient to dissolve one mole of salt, the resulting
solution is supersaturated at the melting temperature. The solid salt, due to its higher density,
settles down at the bottom of the container and the recombination with water during the reverse
process of freezing is not possible. This results in an irreversible melting–freezing of the salt
hydrate that produce low cycling stability; furthermore salt hydrate are corrosive with metal
containers and present subcooling. Table 3.5 shows examples of salt hydrates used as PCM.
22 Chapter 3
Table 3.5 - Examples of salt hydrates that have been investigated as PCM [7]
Material Melting
temperature
[°C]
Melting
enthalpy [kJ/kg]
Thermal conductivity
[W/m∙K]
Density
[kg/m3]
LiClO3∙3H2O 8 155 -
-
1530 (liquid)
1720 (solid)
KF∙3H2O 18.5 231 -
-
1447 (liquid, 20°C)
1455 (solid, 18°C)
CaCl2∙6H2O 29,30 171,190 0.540 (liquid, 39°C)
1.088 (solid, 23 °C)
1562 (liquid, 32°C)
1710 (solid, 25°C)
LiNO3∙3H2O 30 296 -
-
-
-
Na2SO4∙10H2O 32 254 -
0.554
-
1485 (solid)
Na2HPO4∙12H2O 35-44 280 0.476 (liquid)
0.514 (solid)
1442 (liquid)
1522 (solid)
NaS2O3∙5H2O 48-55 187-209 -
-
1670 (liquid)
1750 (solid)
Na(CH3COO)∙3H2O 58 226,264 -
-
1280 (liquid)
1450 (solid)
Ba(OH)2∙8H2O 78 265,280 0.653 (liquid, 86°C)
1.255 (solid, 23°C)
1937 (liquid, 84°C)
2180 (solid)
Mg(NO3)2∙6H2O 89,90 149,163 0.49 (liquid, 95 °C)
0.669 (solid, 56°C)
1550 (liquid, 94
°C)
1636 (solid, 25°C)
MgCl2∙6H2O 117 165,169 0.57 (liquid, 120 °C)
0.704 (solid, 110 °C)
1450 (liquid, 120
°C)
1569 (solid, 20 °C)
Salt
Above 150 ºC, different salts can be used as PCM. The main advantages are very high melting
enthalpy, good thermal conductivity, good chemical stability and very low vapor pressure. The
main drawbacks are subcooling and corrosion of metals. The volume change from solid to liquid
can be up to 10%. Table 3.6 reports a selection of typical examples.
Chapter 3 23
Table 3.6 - Examples of salt that have been investigated as PCM [7]
Material Melting
temperature [°C]
Melting enthalpy
[kJ/kg]
Thermal conductivity
[W/m∙K]
Density
[kg/m3]
LiNO3 254 360 0.58 (liquid)
1.37 (solid)
1780 (liquid)
2140 (solid)
NaNo3 307 172 0.51 (liquid)
0.59 (solid)
1900 (liquid)
2260 (solid)
KNO3 333 266 0.50 (liquid)
-
1890 (liquid)
1900 (solid)
MgCl2 714 452 -
-
2140
-
NaCl 800 492 -
-
2160
-
Na2CO3 854 276 -
-
2533
-
KF 857 452 -
-
2370
-
K2CO3 897 236 -
-
2290
-
Metallics
Metallic PCM includes the low melting metals and metal eutectics. Usually these materials are
used for high temperature applications but their use is extremely limited for PCM thermal energy
storage systems due to the high weight. The main advantages are high heat of fusion per unit
volume, high thermal conductivity and low vapor pressure, while the drawbacks are weight, low
heat of fusion per unit mass and low specific heat. Table 3.7 shows examples of metallics
materials used as PCM.
Table 3.7 - Examples of metallics that have been investigated as PCM [10]
Material Tm [°C] λ [kJ/kg]
Cu(83)-10P-7Si 840 92
Cu(74)-19Zn-7Si 765 125
Cu(91)-9P 715 134
96Zn-4Al 381 138
Mg(55)-28-17Zn 400 146
24 Chapter 3
Zn(49)-45Cu-6Mg 703 176
Mg(52)-25Cu-23Ca 453 184
46.3Mg-53.7Zn 340 185
Cu(80)-20Si 803 197
Zn2Mg 588 230
Mg2Cu 847 243
Mg(60)-25Cu-15Zn 452 254
Mg(84)-16Ca 790 272
34.65Mg-65.35Al 497 285
Al(54)-22Cu-18Mg-6Zn 520 305
Si(49)-30Mg-21Ca 865 305
Al(59)-35Mg-6Zn 443 310
Mg(47)-38Si-15Zn 800 314
64.3-34.0Cu-1.7Sb 545 331
68.5Al-5.0Si-26.5Cu 525 364
60.8Al-33.2Cu-6.0Mg 506 365
Cu(69)-17Zn-14P 720 368
66.92Al-33.08Cu 548 372
64.1Al-5.2Si-28Cu-2.2Mg 507 374
46.3Al-4.6Si-49.1Cu 571 406
Cu(56)-27Si-17Mg 770 420
Al(54)-30Cu-5Si 571 422
86.4Al-9.4Si-4.2Sb 471 471
83.14Al-11.7Si-5.16Mg 555 485
87.76Al-12.24Si 557 498
Si(56)-44Mg 946 757
3.2.3 Eutectics
An eutectic is a mixture of two or more constituents, which solidify simultaneously out of the
liquid at a minimum freezing point, also called eutectic point. At the eutectic point, the liquid
reacts to a solid that is composed of two or more solid phases with different composition;
however, the overall composition is still the same as in the liquid [16]. Therefore, eutectics nearly
always freeze without segregation because they freeze to an intimate mixture of crystals, leaving
Chapter 3 25
little opportunity for the components to separate. Table 3.8 shows examples of eutectics materials
used as PCM.
Table 3.8 - Examples of metallics that have been investigated as PCM [3]
Material Composition (wt. %) Melting point (°C) Latent heat (kJ/kg)
CaCl2∙6H2O+CaBr2∙6H2O 45+55 14.7 140
Triethylolethane+water+urea 38.5+31.5+30 13.4 160
C14H28O2+C10H20O2 34+66 24 147.7
CaCl2+MgCl2∙6H2O 50+50 25 95
CH3CONH2+NH2CONH2 50+50 27 163
Triethylolethane+urea 62.5+37.5 29.8 218
Ca(NO3)∙4H2O+Mg(NO3)3∙6H2O 47+53 30 136
CH3COONa∙3H2O+NH2CONH2 40+60 30 200.5
NH2CONH2+NH4NO3 53+47 46 95
Mg(NO3)3∙6H2O+NH4NO3 61.5+38.45 52 125.5
Mg(NO3)3∙6H2O+MgCl2∙6H2O 58.7+41.3 59 132.2
Mg(NO3)3∙6H2O+MgCl2∙6H2O 50+50 59.1 144
Mg(NO3)3∙6H2O+Al(NO3)∙9H2O 53+47 61 148
CH3CONH2+C17H35COOH 50+50 65 218
Mg(NO3)3∙6H2O+MgBr2∙6H2O 59+41 66 168
Napthalene+benzoic acid 67.1+32.9 67 123.4
NH2CONH2+NH4Br 66.6+33.4 76 151
LiNO3+NH4NO3+NaNO3 25+65+10 80.5 113
LiNO3+NH4NO3+KNO3 26.4+58.7+14.9 81.5 116
LiNO3+NH4NO3+NH4Cl 27+68+5 81.6 108
3.3 Performance of TES systems with PCM
To improve the efficiency of the charging and discharging processes of a PCM-TES system, the
most relevant parameter to be studied is thermal conductivity of the material. In fact, during the
discharging process, the energy released by solidification of the PCM must be transported from
the solid–liquid interface through the growing solid layer to the heat exchanger surface. Hence,
the heat transfer coefficient is dominated by the thermal conductivity of the solid PCM. However,
most PCM usually provide low thermal conductivity around 0.5 W/(m∙K) [23] which results in
poor heat transfer between the HTF and the storage material. In order to increase the thermal
26 Chapter 3
conductivity of PCM, several heat transfer enhancement techniques have been studied (fig. 3.3-
3.4): incorporating high thermal conductivity enhancers into PCM and porous heat transfer media,
extending heat transfer surfaces by fins and capsules, using intermediate heat transfer medium or
heat pipes and employing multiple PCMs.
Fig. 3.3 - Classification of investigated performance enhancement techniques in TES-PCM [24]
Fig. 3.4 - Examples of enhancement techniques in TES-PCM
Chapter 3 27
3.3.1 High-thermal conductivity material enhancers
The heat transfer within a PCM storage system can be enhanced by composing high thermal
conducting material into the PCM. Usually this technique include materials such as ceramic
compound, metal foam and graphite.
Using ceramic compound, the molten PCM is retained and immobilized within the micro-porosity
defined by the ceramic network by capillary forces and surface tension, which offers the potential
of using direct contact heat exchange [25].
Recently, graphite has been studied extensively as heat transfer enhancer in PCM storage systems
due to its high thermal conductivity, low density and chemical resistance [16] [26] [27]. The PCM
graphite composite can be obtained by infiltration/impregnation of PCM within a porous structure
of graphite, dispersion of graphite mechanically within the PCM or compression of the pre-mixed
graphite and PCM [28]. There are numerous commercial available types of graphite, such as
natural graphite flakes, expanded natural graphite and ground expanded natural graphite. Zhao
and Wu [29] [30] experimentally investigated the feasibility of using metal foam and expanded
graphite to enhance the heat transfer capability of NaNO3. The results showed that the heat
transfer rate increase in both charging and discharging phases using this method.
Another technique consist in the insertion of steel lattice or structures with cylindrical or spherical
geometries into the PCM to obtain a melting/solidification time reduction. Drawbacks of this
solution are higher volume and costs.
3.3.2 Extended heat transfer surface enhancers
Extensions of heat transfer surface includes the use of capsules or finned tubes to reduce the
distance for heat transport within the PCM thus improving the heat transfer.
The encapsulation of PCM is divided into macro, micro and nano encapsulation. In macro-
encapsulation, the size of container filled by PCM ranges from several mm up to several cm.
These are often containers and bags made of metal or plastic. Micro-encapsulation is the
encapsulation of solid or liquid particles of 1 μm to 1 mm diameter with a solid shell, while the
capsules smaller than 1 μm are classified as nano-encapsulation. Physical processes used in
micro-encapsulation are spray drying, centrifugal and fluidized bed processes, or coating
processes for example in rolling cylinders. Chemical processes used are in-situ encapsulations
like complex coacervation with gelatine, interfacial polycondensation to get a polyamide or
polyurethane shell, precipitation due to polycondensation of amino resins, and others [16]. If the
rigid capsule is used to contain the PCM, the initial PCM volume should not exceed 80% in order
to compensate the pressure variation during the melting/solidification cycling. There are many
advantages of microencapsulated PCM, such as increasing heat transfer area, reducing PCM
reactivity towards the outside environment and controlling the changes in the storage material
volume as phase change occurs, corrosive to metal, decomposition, sub-cooling and leakage [31].
Fins are used in a large number of applications to increase the heat transfer from surfaces. The fin
is exposed to the PCM, which cools or heats it, with the high thermal conductivity allowing
increased heat being conducted from the wall through the fin. Fins have several shapes but the
28 Chapter 3
most commons are axials and circulars orthogonal to the axis of the heat transfer fluid pipes.
Typically, the fin material has a high thermal conductivity as graphite foil, aluminium, steel and
copper.
3.3.3 Intermediate heat transfer medium enhancers
The concept is based on the reflux created by a combined evaporation–condensation process
occurring in the intermediate HTF. This technology is named Reflux Heat Transfer Storage
(RHTS) system and, it is studied by Adinberg et al. [32] applied to DSG system. Fig. 3.5 reports
the schematic of RHTS storage. HTF is used to transfer heat between the PCM and two heat
exchangers placed externally of the PCM at the bottom and the top and of the storage vessel. The
bottom heat exchanger is immersed in the liquid HTF and connected to the solar working fluid
(water or oil) and it is used during charge phase. The top heat exchanger is a steam generator
which produces superheated steam and it is used during discharge phase. In the charging process,
the liquid HTF absorb energy through vaporization and the vapour flows upwards through the
transport channels distributed in the PCM. Then the vapour condenses on the channel's surfaces
and the latent heat of vapour is released across the walls to the PCM. The liquefied HTF returns to
the pool due to gravity. In the discharging process, the PCM release the energy producing the
evaporation of the liquid HTF. This vapour transfers energy to the HTF passing through the top
heat exchanger [33].
Fig. 3.5 - Reflux heat transfer storage concept
Chapter 3 29
3.3.4 Heat pipe enhancers
The heat pipes are incorporated into the PCM-TES system in order to provide a channel with high
thermal conductivity between the HTF and the PCM (fig. 3.6). The heat pipes transfer heat
between the HTF and the PCM with evaporation and condensation of the heat pipe working fluid
occurring at the ends of the heat pipes. Shabgard et al. [34] investigated the impact of the number
of heat pipes, their orientation relative to the HTF flow direction and the gravity vector in two
distinct system configurations.
Fig. 3.6- Heat transfer between PCM and HTF using heat pipes [34]
3.3.5 Multiple PCM enhancers
In this system, also named cascaded or multi-stage, few modules containing different PCM with
different melting temperatures are connected to each other in series [35] [36] [37]. The multi-
stage configuration is obtained by placing the PCMs in a decreasing order of their transition
temperatures according to flow direction during charge process, while in an increasing order of
their transition temperatures according to flow direction during discharge process as illustrated in
fig. 3.7. The heat transfer rate in the storage systems is mainly dependent on the temperature
difference between the HTF and the PCM. When a single PCM configuration is used, this
temperature difference decreases in the HTF flow direction, consequently also the heat transfer
rate decreases. When a multiple PCM configuration is used, the temperature difference can be
maintained approximately constant because both the HTF temperature and the melting point of
the PCM decrease in the HTF flow direction during the charging process. During discharge both
of them increase in the HTF flow direction. Therefore, the heat flux from the PCM to the HTF is
nearly constant during the entire process.
30 Chapter 3
Fig. 3.7- Multiple PCM configuration in thermal energy storage systems
Chapter 4 31
Chapter 4
Mathematical models of the PCM thermal
energy storage system
4.1 Introduction
In this thesis, different n-dimensional numerical models were developed with the COMSOL
Multiphysics 5.0 platform in order to simulate the transient and energy behaviour of different
geometries and configuration of PCM-TES systems during the phase change processes. COMSOL
Multiphysics is a software package for analysis, simulation and solver applied to various physical
and engineering applications, especially coupled phenomena, or multiphysics based on finite
elements method.
Two different approaches both in accordance with the apparent heat capacity formulation were
evaluated and presented. In the first approach the energy equation was solved considering heat
transfer only by conduction in liquid PCM domain. For this case, a 3D numerical simulation code
was developed to simulate the thermal energy storage system based on the configuration of the
shell and tube heat exchanger.
In the second approach the energy equation was solved considering heat transfer by heat
conduction and natural convection in liquid PCM domain. The Boussinesq approximation was
introduced to consider the buoyancy force. For this case, a 2D axysimmetric numerical code was
developed comparing different configurations of TES (double tube, double tube with fins and
triplex with fins). Furthermore the effect of the number of fins on the PCM melting time was
investigated.
Finally, a 2D axysimmetric numerical model of a double tube heat exchanger with fins was
validated considering the two different approaches. The purpose of this analysis was focused both
on the performance evaluation of different TES configurations and on the evaluation of which
mathematical model presents more accuracy to simulate the real behaviour of these systems.
4.2 Mathematical models
The phenomena of melting and solidification are associated with many practical applications, not
only in thermal energy storage systems but also in several industrial processes, such as metal
processing, solidification of castings and environmental engineering, in food and pharmaceutical
processing. Predicting the behaviour of phase transition is difficult due to its non-linear nature at
moving boundary and also because PCM materials show thermo-physical properties which vary
32 Chapter 4
according to the phase. The term ‘moving boundary problems’ is associated with time-dependent
problems, where the position of the moving boundary must be determined as a function of time
and space. The analysis of heat transfer related to phase transition problems is called Stefan
problem. The Stefan problem was first investigated as pure conduction and later natural
convection was considered during melting and solidification of PCM [38]. Analytical and
numerical methods are used to solve Stefan problem.
Analytical solutions of melting and solidification problems require many simplification and
approximations, are generally one-dimensional, consider heat transfer only by conduction, apply
simple boundary and initial conditions and constant thermo-physical properties. Moreover,
analytical solutions can be rigorously valid for semi-infinite domains only. Therefore, these
results are used to provide basic knowledge of the phenomena as well as the basis for validation
of more complicated theoretical and numerical schemes.
Due to these simplifying assumptions, the use of numerical methods is required to obtain more
accurate solutions of the problem for most applications of practical interest. Therefore, ad-hoc
codes for specific applications or commercial software adapting to the PCM behaviour during
transition phase must be used and developed.
The finite elements method (FEM) is the numerical method most commonly used, but also finite
difference method (FDM), boundary element method (BEM), the Monte-Carlo and others are
used. The success of finite element and boundary element methods lies in their ability to handle
complex geometries, while the time consuming in terms of computing and programming is the
main drawback. These methods can be divided into front-tracking methods and fixed-domain
methods.
Front tracking methods:
Fixed mesh, finite difference
Variable mesh, finite difference
Moving mesh, finite element
Moving boundary element
Fixed domain methods:
Apparent heat capacity
Enthalpy based formulations
Apparent heat capacity with post-iteration correction
Fictitious heat flow
Freezing index
Discontinuous integration
In this thesis, the phase change processes were treated using fixed domain method based on
apparent heat capacity. This method will be explained in paragraph 4.2.1.
4.2.1 Apparent heat capacity formulation
The apparent heat capacity formulation assumes that the latent heat is evaluated by increasing the
heat capacity of the material in a transition temperature range. For instance, in a solid-liquid
transition, if the latent heat is released uniformly in the phase change temperature range, the
apparent heat capacity is given by:
Chapter 4 33
𝐶𝑝,𝑎𝑝𝑝 =
{
𝐶𝑝,𝑠𝑜𝑙
[∫ 𝐶𝑝(𝑇)𝑑𝑇 + 𝐿𝑓𝑇𝑙𝑖𝑞𝑇𝑠𝑜𝑙
]
(𝑇𝑙𝑖𝑞 − 𝑇𝑠𝑜𝑙)
𝐶𝑝,𝑙𝑖𝑞
𝑇 < 𝑇𝑠𝑜𝑙
𝑇𝑠𝑜𝑙 < 𝑇 < 𝑇𝑙𝑖𝑞
𝑇 < 𝑇𝑙𝑖𝑞
solid phase
solid/liquid phase
liquid phase
(4.1)
Where 𝐶𝑝,𝑠𝑜𝑙 and 𝐶𝑝,𝑙𝑖𝑞 are specific heat of solid and liquid phase respectively, 𝑇𝑙𝑖𝑞 and 𝑇𝑠𝑜𝑙 are
the temperature of solid and liquid phase respectively, 𝐶𝑝(𝑇) is the specific heat during transition
in function of the temperature, while 𝐿𝑓 is the latent heat of fusion. Figure 4.1 reports the apparent
heat capacity in function of temperature.
Fig. 4.1- Smoothed function used to evaluate Cp in apparent heat capacity formulation
Using these definitions, the energy equation for the entire region is defined as:
𝜌𝐶𝑝,𝑎𝑝𝑝𝜕𝑇
𝜕𝑡+ 𝜌𝐶𝑝,𝑎𝑝𝑝𝑢 ∙ 𝛻𝑇 = 𝛻 ∙ (𝑘𝛻𝑇) (4.2)
Where:
𝜌 is the density [kg/m3]
𝑢 is the fluid velocity (PCM in liquid phase) [m/s]
𝐶𝑝,𝑎𝑝𝑝 is the specific heat evaluated with Equation (4.1) [J/kg∙K]
𝑘 is the thermal conductivity [W/m∙K]
𝑇 is the temperature [K]
𝑡 is the time [s]
34 Chapter 4
The first term represents the rate of temperature change in function of time, the second and the
third terms represent the heat transfer by conduction and by convection respectively.
Equation (4.2) can easily be discretized and solved numerically. The apparent heat capacity
formulation was first applied using a finite difference method based on the Crank–Nicolson
scheme for one-dimensional problems [39] where the phase change occurs in a finite temperature
interval. Then it was applied using the finite element method in a generally applicable approach to
one and two-dimensional problems with both moving boundary and temperature-dependent
physical properties [40].
The apparent heat capacity formulation is conceptually simple and one of this advantages is that
temperature is the primary dependent variable that derives directly from the solution. However, it
is well known that this formulation presents an important drawback with respect to the other
methods [41] when the phase change transition occurs at a fixed temperature. During melting
process, if the temperature of a control volume rises from below the solidus to above the liquidus
temperature in one time step, the absorption of the latent heat for that control volume is not
accounted for. Same difficulty also occurs during solidification process. This problem can be
overcome by assuming that the phase change occurs over a small temperature range and very
small time steps have to be used during transition. All PCM considered in this thesis are not pure
substances, whereby phase transition takes place not at a fixed temperature but in a range
temperature. The use of the apparent heat capacity method is therefore justified.
4.3 First approach: 3D numerical model
4.3.1 Material and method
A 3D numerical simulation code of a PCM-TES during both charging and discharging processes
was developed considering the first approach.
The geometry adopted for the storage system is presented in figure 4.2 and it is based on the
configuration of the shell and tube heat exchanger. Shell is filled with PCM while the working
fluid flows in the tube side. The choice of this configuration was made taking into account that a
similar storage system will be used for the experimental investigations with the test rig
implemented in the laboratory for TES technologies of the DIMCM-University of Cagliari. The
design of the test rig and of the TES are treated in chapter 5.
Chapter 4 35
Fig. 4.2 - Geometrical configuration of TES system
For this model, Hydroquinone was selected among different PCM candidates after a literature
review [9][16][23][42][43] since it has a phase change temperature range between 166 °C and 173
°C and a melting enthalpy of 225 kJ/kg [9]. Many applications exist in this temperature range
such as in solar technologies generally associated with Organic Rankine Cycle (ORC) or in solar
cooling systems with absorption chiller, related to fuel cell PAFC, heat recovery in metal hydrides
hydrogen storage systems, in the food, beverage, transport equipment, textile, machinery, pulp
and paper industries and drying of agricultural products as reported in Table 1.3.
Hydroquinone is an aromatic organic compound that is a type of phenol, a derivative of benzene,
having the chemical formula C6H4(OH)2. This material was chosen because its properties and
features are easy to find in the literature and could be readily used for calculation. However,
Hydroquinone presents an important drawback concerning the toxic hazards: its mutagenic and
carcinogenic properties make it inappropriate in laboratory activities. Therefore, different
materials, most suitable for laboratory activities, were also selected for the other analysis
presented in this thesis. The properties of Hydroquinone are shown in Table 4.1 [44].
Table 4.1 - Properties of Hydroquinone
Solid Liquid
Density (kg/m3) 1358 1155
Specific heat (J/kg·K) 2310 2670
Thermal conductivity (W/m·K) 0.45 0.612
Phase change temperature 172.4 °C
Range phase transition temperature 3 °C
Latent heat 225 kJ/kg
Boling point 285 °C
Flash point 165 °C - closed cup
pH 3.7 at 70 g/l
36 Chapter 4
The "Therminol66" from Solutia Inc. was selected as heat transfer fluid (HTF) as it covers an
operating range suitable with the process under study.
The design of the storage system was based on the Logarithmic Mean Temperature Difference
(LMTD) method and calculations were made using Matlab. The geometrical characteristics and
the operating parameters of the TES are shown in Table 4.2.
Table 4.2 - Geometrical characteristics and operating parameters of storage system
Units Value
Diameter m 0.127
Length m 2.44
Number of tubes - 17
Number pass of tubes - 1
Internal diameter of tubes m 0.0135
External diameter of tubes m 0.0191
HTF mass rate kg/s 0.11
PCM mass kg 104
HTF temperature inlet charge °C 200
HTF temperature inlet discharge °C 100
The mesh used (Fig. 4.3) is built with 71731 free tetrahedral elements with size between 4.88∙10-4
m and 4.88∙10-2
m. The smallest elements of the mesh are used in the HTF inlet and outlet section
in the system and to create a boundary layer around the tube and in the edges of the PCM. Axially
in the outer surfaces of the PCM, where extreme precision is not required in the calculation of the
temperature gradients, the largest elements of the mesh are used.
Fig. 4.3 - Mesh using for the TES simulation
Chapter 4 37
The numerical model based on the first approach was developed to simulate the transient
behaviour of the PCM-TES and to evaluate the TES overall performances. Two different
“physics”, described in the following, were used to create the model. The first physics "Non-
Isothermal Pipe Flow" was used to simulate the pipes, the second "Heat Transfer with Phase
Change" was used to simulate the PCM behaviour.
The following assumptions are applied:
The velocity profile is fully developed and does not change within a section.
Laminar flow
Uniform temperature at inlet
The cross section area is allowed to change between pipe segments.
Empirical functions describe viscous losses.
PCM is bounded by adiabatic external wall
Non-Isothermal Pipe Flow
This module defines the conservation of mass, momentum and energy of a fluid inside the pipes
(Eq. 4.3-4.5). The mass flow, pressure, temperature and concentration fields across the pipe
sections are modelled as cross-section averaged quantities, which only vary along the length of
the pipes. The pressure losses along the length of the pipes are described using Darcy friction
factor expression. The energy balance equations are solved assuming heat transfer by convection
and conduction, and the flow is considered incompressible.
𝛿𝐴𝜌
𝛿𝑡+ ∇𝑡 ∙ (𝐴𝜌𝑢𝑒𝑡) = 0 (4.3)
𝜌𝛿𝑢
𝛿𝑡= −𝛻𝑡𝑝 ∙ 𝑒𝑡 −
1
2𝑓𝐷
𝜌
𝑑ℎ|𝑢|𝑢 (4.4)
𝜌𝐴𝐶𝑝𝛿𝑇
𝛿𝑡+ 𝜌𝐴𝐶𝑝𝑢𝑒𝑡 ∙ 𝛻𝑡𝑇 = 𝛻𝑡 ∙ (𝐴𝑘𝛻𝑡𝑇) +
1
2𝑓𝐷𝜌𝐴
𝑑ℎ|𝑢|𝑢2 + 𝑄𝑤 (4.5)
where:
𝐴 is the pipe cross section area available for flow [m2]
𝜌 is the density [kg/m3]
𝑡 is the time [s]
𝑢 is the cross section averaged velocity [m/s]
𝑒𝑡 = (𝑒𝑡,𝑥𝑒𝑡,𝑦𝑒𝑡,𝑧) is the unit tangent vector to the pipe axis
𝑝 is the pressure [Pa]
𝑓𝐷 = 𝑓𝐷(𝑅𝑒, 휀/𝑑ℎ) is the Darcy friction factor. This parameter accounts for the
continuous pressure drop along a pipe segment due to viscous shear, and is expressed as a
function of the Reynolds number and the surface roughness divided by the hydraulic
diameter. Thus, the second term on the right-hand side in Equation 4 represents the
pressure drop due to viscous shear
38 Chapter 4
𝑅𝑒 = 𝜌𝑢𝑑ℎ 𝜇⁄ is the Reynolds number
𝜇 is the dynamic viscosity [Pa∙s]
𝑑ℎ = 4𝐴 𝑍⁄ is the mean hydraulic diameter [m]
𝐴 is the pipe cross section area available for flow [m2]
𝑍 is the wetted perimeter [m]
𝑇 is the temperature [K]
𝑄𝑤 is the external heat exchange through the pipe wall [W/m] given by:
𝑄𝑤 = (ℎ𝑍)𝑒𝑓𝑓(𝑇𝑒𝑥𝑡 − 𝑇) (4.6)
In Equation 4.6, (ℎ𝑍)𝑒𝑓𝑓 is an effective value of the heat transfer coefficient h [ W/m2·K]
multiplied by the wall perimeter Z of the pipe. Text [K] is the external temperature outside of the
pipe.
Heat Transfer with Phase Change
The energy equation (4.2), in accordance with the apparent heat capacity formulation is used to
obtain the temperature field in PCM domain. Instead of adding a latent heat 𝐿𝑓 in the Equation
(4.2) when the material reaches its phase change temperature 𝑇𝑚, it is assumed that the transition
occurs in a temperature interval between (𝑇𝑚 − ∆𝑇𝑚 2)⁄ and (𝑇𝑚 + ∆𝑇𝑚 2)⁄ . In this range the
material phase is modelled by a smoothed function α, representing the fraction of phase that
generates during transition. The value of this function is equal to 0 before (𝑇𝑚 − ∆𝑇𝑚 2)⁄ and to 1
after (𝑇𝑚 + ∆𝑇𝑚 2)⁄ . The enthalpy H is expressed by:
𝐻 = (1 − 𝛼)𝐻𝑝ℎ𝑎𝑠𝑒1 + 𝛼𝐻𝑝ℎ𝑎𝑠𝑒2 (4.7)
where 𝐻𝑝ℎ𝑎𝑠𝑒1 and 𝐻𝑝ℎ𝑎𝑠𝑒2 are the enthalpies of the material related to phase 1 or phase 2,
respectively. Differentiating with respect to temperature, the following formula for the specific
heat capacity is obtained:
𝐶𝑝 = (1 − 𝛼)𝑑
𝑑𝑇(𝐻𝑝ℎ𝑎𝑠𝑒1) + 𝛼
𝑑
𝑑𝑇(𝐻𝑝ℎ𝑎𝑠𝑒2) + (𝐻𝑝ℎ𝑎𝑠𝑒2 −𝐻𝑝ℎ𝑎𝑠𝑒1)
𝑑𝛼
𝑑𝑇 (4.8)
which can be rewritten as:
𝐶𝑝 = (1 − 𝛼)𝐶𝑝,𝑝ℎ𝑎𝑠𝑒1 + 𝛼𝐶𝑝,𝑝ℎ𝑎𝑠𝑒2 + (𝐻𝑝ℎ𝑎𝑠𝑒2 −𝐻𝑝ℎ𝑎𝑠𝑒1)𝑑𝛼
𝑑𝑇 (4.9)
Chapter 4 39
In Equation (4.9) the third term of the second member is the distribution of latent heat:
𝐶𝐿(𝑇) = (𝐻𝑝ℎ𝑎𝑠𝑒2 −𝐻𝑝ℎ𝑎𝑠𝑒1)𝑑𝛼
𝑑𝑇 (4.10)
In the ideal case, when the PCM is a pure substance, 𝛼 is the Heaviside function (equal to 0
before 𝑇𝑚 and to 1 after 𝑇𝑚), the term 𝑑𝛼 𝑑𝑇⁄ corresponds to the Dirac pulse. Therefore, 𝐶𝐿 is the
enthalpy jump 𝐿𝑓 at temperature 𝑇𝑚 that is added to specific heat capacity. The Equation (4.10) is
approximated by:
𝐶𝐿(𝑇) = 𝐿𝑓𝑑𝛼
𝑑𝑇 (4.11)
so that the total heat per unit mass released during the phase transition corresponds to the latent
heat:
∫ 𝐶𝐿(𝑇)𝑑𝑇𝑇𝑚+∆𝑇 2⁄
𝑇𝑚−∆𝑇 2⁄
= 𝐿𝑓∫𝑑𝛼
𝑑𝑇𝑑𝑇
𝑇𝑚+∆𝑇 2⁄
𝑇𝑚−∆𝑇 2⁄
= 𝐿𝑓 (4.12)
Finally, the apparent heat capacity 𝐶𝑝,𝑎𝑝𝑝 is given by:
𝐶𝑝,𝑎𝑝𝑝 = (1 − 𝛼)𝐶𝑝,𝑝ℎ𝑎𝑠𝑒1 + 𝛼𝐶𝑝,𝑝ℎ𝑎𝑠𝑒2 + 𝐿𝑓𝜕𝛼
𝜕𝑇 (4.13)
The equivalent heat conductivity and density are given by Equations (4.14) and (4.15)
respectively:
𝑘 = (1 − 𝛼)𝑘𝑝ℎ𝑎𝑠𝑒1 + 𝛼𝑘𝑝ℎ𝑎𝑠𝑒2 (4.14)
𝜌 =(1 − 𝛼)𝜌𝑝ℎ𝑎𝑠𝑒1𝐶𝑝,𝑝ℎ𝑎𝑠𝑒1 + 𝛼𝜌𝑝ℎ𝑎𝑠𝑒2𝐶𝑝,𝑝ℎ𝑎𝑠𝑒2
(1 − 𝛼)𝐶𝑝,𝑝ℎ𝑎𝑠𝑒1 + 𝛼𝐶𝑝,𝑝ℎ𝑎𝑠𝑒2 (4.15)
40 Chapter 4
These equations allow to evaluate the HTF behaviour, the heat transfer that occur in the entire
model (in PCM domain only the heat transfer by conduction is considered) and the PCM
thermophysical properties in both liquid and solid phase.
4.3.2 Results and discussion
In this paragraph the results of simulations performed on 3D model using the first approach are
presented. Figures 4.4(a,b) show the temperature profiles during charge and discharge phase. The
initial condition chosen assumes the temperature of the entire system (PCM, tubes, and HTF)
equal to 100 °C. This condition was assumed to simulate a charging process starting from a
homogeneous initial state of the PCM. In this way it is possible to clearly observe the phase
transition of the PCM in the sections closest to the HTF inlet. Then, after 1 min, the HTF
temperature is assumed to increase up to a value of 200 °C with a step function thus, the charging
process starts (Fig. 4.4a). The discharging process is performed analogously. At the beginning, the
entire system temperature is equal to 200 °C, then, after 1 min, the HTF temperature suddenly
decreases up to 100 °C and the discharging process begins (Fig. 4.4b).
(a) (b)
Fig. 4.4 - Profiles of PCM temperature for (a) charge phase, and (b) discharge phase
In the charge phase the transition process finishes after approximately 3 hours while in the
discharge phase the complete transition is reached in about 1 hour. As expected, the melting
process took more time than the solidification due to the lower difference between the phase
change temperature of the PCM and the HTF temperature, being approximately 25°C and 70°C
(absolute values), respectively.
Figures 4.5 and 4.6 show the phase change evolution for three different time steps during charge
and discharge respectively. Three different sections of the TES are represented: the inlet, the mid
Chapter 4 41
and the outlet section starting from the left. The red area represents the solid phase of the PCM
material, the blue area represents the liquid phase while the tubes are reported as black lines. The
first time step is selected to show the existing condition in the three section considered when in
the outlet section begins the transition process. Instead, the third time step is selected to show the
condition in which the PCM has completely terminated the transition phase in the inlet section.
The second time step represents approximately an intermediate time between the beginning and
the end of the phase transition
60 min
100 min
150 min
Fig. 4.5 - Profiles of PCM temperature and solid-liquid interface evolution in the charge phase
As expected the PCM phase change starts in proximity of the tubes, then continues in the
intersections between them, and finally near the wall of the shell. It can be notice that the in the
central part of the TES, the melting process proceeds more quickly than in the external part owing
to the different tube pitch chosen for this configuration as reported in Figure 4.5. It is evident that
42 Chapter 4
lower the tube pitch, greater the thermal interaction between the tubes that allows a greater heat
transfer rate released to the PCM. When the phase transition begins to be detected in the inlet
section, it takes approximately 4 minutes for melting to propagated up to the outlet section. After
100 minutes, melted PCM is in the area enclosed by the tube in the inlet section, while in the
outlet section the solid-liquid front has not yet reached the outer tubes. After 150 minutes the
PCM in the inlet section is completely in liquid state, while in the mid and in the outlet section,
areas with PCM in solid state already exist near the external wall. When in the inlet section the
complete melting is achieved, it needs another 40 minutes to reach the complete transition in the
outlet section.
15 min
40 min
75 min
Fig. 4.6 - Profiles of PCM temperature and solid-liquid interface evolution in the discharge
phase
Chapter 4 43
Figure 4.6 shows, in a similar way of figure 4.5, the phenomena of solidification during the
discharge phase. Also in this case, the pitch tube influences the transition process. After 15
minutes a PMC in solid state is observed in the inlet section, while in the outlet section only very
small areas around the tubes are observed. After 40 minutes the solid-liquid interface moves from
the center to the external wall of the TES. After 75 minutes, in the inlet section the PCM is
completely solidified, while the mid and the outlet section still presents areas of liquid PCM in
proximity of the external wall.
The shape of solid-liquid interface depends on the heat transfer process considered. The solid-
liquid interface moves uniformly around the tubes because the convection and the buoyancy force
were not considered with this approach. Another parameter that depends on heat transfer process
is the melting and solidification time. In fact, convection improves the heat transfer between
liquid and solid PCM decreasing the charge and the discharge phase time.
Further considerations about the shape and the motion solid-liquid interface and the effects of the
natural convection will be presented in the following paragraphs. The comparison between the
heat transfer only by conduction and the heat transfer by both conduction and convection is
discussed by validating the two approaches discussed.
4.4 Second approach: 2D axysimmetric numerical model
4.4.1 Introduction
Several researches investigate the role of natural convection that occurs in the phase transition of
a PCM during thermal energy storage. The literature includes studies on both numerical methods
and different storage system configurations. The first are based on reproducing the time evolution
of the solid-liquid interface during a melting and solidification process taking into account the
natural convection phenomena. The latter are based on the development of different TES
configuration to optimize the amount of exchanged heat. Longeon et al. [45] conducted an
experimental and numerical study about the annular PCM solidification and melting system. The
results show that in vertical TES the motion direction of the HTF into the TES, related to the
natural convection heat transfer mechanism, affects the development of the PCM melting front.
Furthermore, the configuration in which the HTF enters from above during the charging process
and from the bottom during discharging process is recommended. Ismail and Da Silva [46]
proposed a model for melting PCM around a horizontal circular cylinder, including heat transfer
by convection. Agyenim et al. [47] and Dubovsky et al. [48] studied configuration of finned shell
and tube heat exchanger storage systems. Castell et al.[49] determined the heat transfer coefficient
by natural convection for a cylindrical module with external fins using experimental correlations.
Khalifa et al. [50] conducted experimental and numerical investigations on the thermal
performance of LHTES systems based on heat pipes for solar thermal power generation proving
the benefits of added fins. Zhang and Faghri [51] analyzed numerically the heat transfer
enhancement in LHTES systems using internal finned tube. The results indicate that the melting
fraction can be significantly increased by increasing the thickness, height and number of fins.
44 Chapter 4
4.4.2 Material and method
Three cases with different geometrical configurations (Fig. 4.7a,b,c) were considered in
characterizing the TES system using the second approach:
- Case 1 (Fig. 4.7a) is based on the configuration of the double-tube heat exchanger, where the
outer tube is filled with PCM while the heat transfer fluid (HTF) flows in the inner tube.
- Case 2 (Fig. 4.7b) is based on a triplex heat exchanger. It is composed of three tubes: the
HTF flows in the outer and inner tubes, while the PCM is placed between them.
- Case 3 (Fig. 4.7c) is a triplex with circular fins with pitch ratio equal to 0.142 (Fin pitch ratio
refers to the spacing between centerlines of fins divided by the TES length ).
For the present study, D-Mannitol was selected from among different PCM candidates after a
literature review [2][3][16][42][43][52] since it has a phase change temperature range between
164 and 170 °C. As for the Hydroquinone, in fact, also this material was selected in a operating
temperature range between 150-200 °C where many applications exist such as in solar
technologies generally associated with Organic Rankine Cycle (ORC) or in solar cooling systems
with absorption chiller, related to fuel cell PAFC, heat recovery in metal hydrides hydrogen
storage systems, in the food, beverage, transport equipment, textile, machinery, pulp and paper
industries and drying of agricultural products as reported in Table 1.3.
D-Mannitol is classified as a sugar alcohol, molecular formula C6H14O6: it is derived from a sugar
(mannose) by reduction. The properties of D-Mannitol are shown in Table 4.4. Thermophysical
properties of the liquid phase were obtained from other materials belonging to the same family
and with similar transition temperatures with an estimated uncertainty of about 10%. Although
widely used in other fields (pharmaceuticals, food industry etc.), only in recent years has this kind
of materials been studied and used for thermal energy storage.
Due to its safety and its good thermophysical properties for thermal energy storage, D-mannitol
was also selected as PCM for the experimental tests that will be performed in the DIMCM
laboratories. As concerns latent heat, a value of 316 kJ/kg was found in literature [16], obtained
for the pure substance and under controlled conditions, but several tests with the DSC
[53][54][55][56][20] detected that this value depends strongly on three important factors, namely
purity, cooling/heating rate and air contact. For these reasons, a more "realistic" value of 234
kJ/kg c was used in this work [16][54][55][56][57].
Table 4.3 - Properties of D-Mannitol.
Solid Liquid
Density (kg/m3) 1520 (20 °C) 1382
Specific heat (kJ/kg·K) 1.320 (20 °C) a 1.452
Thermal conductivity (W/m·K) 0.279 b 0.307
Phase change temperature 167°C
Range of phase transition temperature ±3°C
Latent heat 234 kJ/kg c a NIST web page (National Institute of Standards and Technology). b Thermal Energy Storage Systems for Solar Cookers, www.ukessays.com c value obtained as the average of the experimental results found in literature
[16][54][55][56][57].
Chapter 4 45
Syltherm800 from Dow Chemical Company was selected as the heat transfer fluid, as it is the
HTF used in the experimental facility implemented in the laboratory for TES technologies of the
DIMCM-University of Cagliari.
Syltherm800 is a highly stable, long-lasting, silicone fluid designed for high-temperature liquid
phase operation. It has a recommended operating temperature range between -40°C and 400°C.
The main advantages of this oil are low fouling potential, low freeze point, high-temperature
stability, long life, non-corrosive, low acute oral toxicity and low odour. At elevated temperatures,
it is sensitive to contamination. Contamination by acids or bases can result in accelerated rates of
volatile by-product formation, while contamination by water, oxygen, or other oxidants can result
in crosslinking of polymer molecules, that can cause a gradual increase in viscosity. Thus, it is
important that contamination be minimized [58].
(a) Case 1 - Double tube (b) Case 2 - Triplex (c) Case 3 - Triplex with fins
Fig. 4.8 - Geometrical configuration of the three TES systems.
The design of the storage systems is based on the LMTD method and was performed by means of
a computer code developed in Matlab environment. The geometrical characteristics of the three
TESs are shown in Table 4.3. The value of HTF mass flow rate was selected as 0.052 kg/s for all
three cases analyzed for both charge and discharge phases. In the triplex heat exchanger the flow
rate is equally divided between inner and outer tube. Consequently, due to the different surface
areas, the velocities results different and equal to 0.0664 m/s and 0.0049 m/s for inner and outer
tube respectively. The HTF temperature at the inlet of the storage device was chosen equal to 180
°C and 100 °C for charge and discharge respectively. The HTF flows from top to bottom during
both charge and discharge phases. The PCM mass for Cases 1 and 2 was 23.4 kg, while for Case
3, owing to the space occupied by the fins, the value was slightly lower, 22.8 kg, allowing a
thermal energy storage of about 3 kWh.
46 Chapter 4
Table 4.4 - Geometrical characteristics of the storage system
Case 1 Case 2 Case 3
Heat transfer surface [m2] 0.077 0.568 0.73
Internal Diameter inner tube [m] 0.0254 (1'') 0.0254 (1'') 0.0254 (1'')
Outside Diameter tube PCM [m] 0.127 (5'') 0.127 (5'') 0.127 (5'')
Outside Diameter outer tube HTF [m] - 0.1898 0.1898
Length [m] 0.83 0.83 0.83
Number of fins - - 6
Fin Length [m] - - 0.05
Fin thickness [m] - - 0.005
Tube thickness (Steel) [m] 0.002 0.002 0.002
A 2D axisymmetric numerical model using the second approach was developed with the
COMSOL Multiphysics platform to simulate the transient and energy behaviour of the entire
PCM-TES system during the phase change processes. Three different “physics”, described below,
were used to create the model:
- the first and the third physics, "Fluid Flow", were used to simulate the behaviour of the HTF
and the liquid PCM;
- the second, "Heat Transfer", was used to simulate the heat transfer process between the HTF
and the PCM; it is composed of three sub-modules: heat transfer by convection, by
conduction and phase change heat transfer.
The mathematical model is based on the following hypothesis:
- Two-dimensional and axisymmetric problem.
- The velocity profile is fully developed and does not change within a section.
- Laminar flow
- Uniform temperature at inlet
- The cross section area is allowed to change between pipe segments.
- Empirical functions describe viscous losses.
- PCM is bounded by adiabatic external wall
Fluid Flow (HTF)
To simulate the dynamic behaviour of the HTF flowing inside the inner tube (Case 1) and inside
the inner and the outer tubes (Case 2-3), the continuity equation (4.15) and the momentum
equation (4.16) were used. The flow is considered laminar and incompressible and the effect of
gravity is negligible (𝐹=0).
𝜕𝜌
𝜕𝑡+ ∇ ∙ (𝜌𝑢) = 0 (4.15)
𝜕𝜌𝑢
𝜕𝑡+ 𝜌(𝑢 ∙ ∇)𝑢 − ∇ ∙ [μ(∇u + (∇u)T)] + ∇𝑝 = 𝐹 (4.16)
Chapter 4 47
where:
𝜌 is the density[kg/m3]
𝜇 is the dynamic viscosity [Pa∙s]
𝑢 is the velocity vector [m/s]
𝑝 is the pressure [Pa]
𝐹 is the volume force [N/m3]
𝑇 is the absolute temperature [K]
𝑡 is the time [s]
In Equation (4.16) the first two terms correspond to the inertial forces, the third term corresponds
to viscous forces, the forth represents the pressure forces and the first term at second member
corresponds to the external forces applied to the fluid.
Heat Transfer in Fluid
Heat transfer from the HTF to the wall of the steel tube takes place by convection. The energy
equation (4.17) was solved using the velocities found from the solution of Eqs. (4.15) and (4.16).
In Equation (4.17) 𝐶𝑝 and 𝑘 are respectively the specific heat and the thermal conductivity of the
material.
𝜌𝐶𝑝𝜕𝑇
𝜕𝑡+ 𝜌𝐶𝑝𝑢 ∙ ∇𝑇 = ∇ ∙ (𝑘∇𝑇) (17)
Heat Transfer in Solid
Heat transfer from the wall of the steel tube to the PCM takes place by conduction. The energy
equation (4.17) for this case is reported below:
𝜌𝐶𝑝𝜕𝑇
𝜕𝑡= ∇ ∙ (𝑘∇𝑇) (4.18)
Heat Transfer with Phase Change
Also for this case, the energy equation (4.2), in accordance with the apparent heat capacity
formulation (Eq. 4.12), was used to obtain the temperature field and the PCM properties (Eqs
4.13-4.14).
Fluid Flow (liquid PCM)
The continuity (4.15) and momentum (4.16) equations were used to simulate the behaviour of the
PCM in liquid phase. To simulate the buoyancy force giving rise to natural convection, a volume
force was added. The Boussinesq approximation was introduced to consider this buoyancy force,
according to Equation (4.19). In this case 𝜌, 𝜇 and 𝛽 are respectively the density, the dynamic
48 Chapter 4
viscosity and the thermal expansion coefficient of the liquid PCM [1/K], g is the gravitational
constant [m/s2] and 𝑇𝑚 is the melting temperature. The flow is considered laminar and
incompressible.
𝐹𝑏 = 𝑔𝜌𝛽(𝑇 − 𝑇𝑚) (4.19)
In this approach, the entire PCM was treated as a liquid, even when its temperature was lower
than its melting point. A modified viscosity was used to force this liquid to behave as a solid
when required. A step function, continuous second derivative centred at about 𝑇𝑚, was introduced
to define the modified viscosity: an extremely large value was selected for the solid PCM and the
actual value of 𝜇 was selected for the liquid PCM [59]. This approach forces the Navier-Stokes
equation to calculate the velocity everywhere, even when the PCM is a solid. This significantly
increases the number of calculations and the possibility that the solver will diverge during the
simulation. A second volume force, defined by Eq. (4.20), was added to the momentum equation
to calculate velocities equal to zero in the solid phase of PCM.
𝐹𝑣 = −𝐴(𝑇) ∙ u (4.20)
In this equation a step function 𝐴(𝑇) was introduced: its value was extremely large for the solid
PCM and zero for the liquid PCM [59]. The role of 𝐹𝑣 is to dominate every other force terms in
the momentum equation (4.16) when the PCM is solid, thus improving the time of calculation and
effectively forcing a trivial solution of 𝑢 = 0 in the solid. This method is mathematically better
defined and allows a reduction of the number of iterations performed by the solver.
4.4.3 Results and discussion
In this paragraph the simulation results of the three cases considered are presented. Figure 4.6
shows the temperature evolution of the PCM evaluated at the bottom of the accumulator (in
proximity of the HTF outlet), in function of time during charge (Fig. 4.6a) and discharge (Fig.
4.6b). In charging mode, the process started from a homogeneous initial state of the entire system
(PCM, tubes, and HTF). At the beginning, the entire PCM system was at the set temperature of
100 °C, with an inlet temperature of the HTF of 180 °C. In this condition the heat transfer inside
the solid PCM was governed by conduction. Then, when the temperature range of phase transition
was reached, the melting process began. During the phase transition both conduction and natural
convection in liquid phase occurred. At the end of the transition process, the heat transfer inside
the liquid PCM was governed by convection.
Chapter 4 49
(a) (b)
Fig. 4.8 - PCM temperature profile for charge (a) and discharge (b) processes.
The discharging process was performed analogously. Initially, the entire PCM system was at the
set temperature of 180 °C, with an inlet temperature of the HTF of 100 °C. The duration of the
charge and discharge processes was imposed as 12 and 8 hours respectively. In the charge phase
the transition process finished after approximately 9-10 hours, while in the discharge phase the
complete transition was reached in about 3.5 hours. As expected, the melting process took longer
than solidification owing to the lower temperature difference between PCM during transition and
HTF at the accumulator inlet, approximately 15 °C during charge and 70 °C during discharge.
Case 3 presents the lowest time of charge and discharge, owing to the enhanced heat transfer
surface which allows the exchange of higher and more uniform thermal power with respect to the
other cases. Fig. 4.8 points out that neither in the charging nor in the discharging phase does Case
1 reach the equilibrium condition for melting/solidification respectively. In fact, after 12 hours of
charge and 8 hours of discharge, the PCM shows a lower temperature value than the HTF
temperature at TES inlet equal to 180 °C and 100 °C for charge and discharge respectively.
Therefore, in this case the charge and the discharge processes are much slower than in the other
two cases. The dashed line refers to the condition where Case 1 continues for 12 hours as for the
charge phase.
50 Chapter 4
80 min 200 min 460 min 20 min 120 min 215 min
Case
1
(a) (b)
Case
2
(c) (d)
Case
3
(e) (f)
Fig. 4.9 - Phase evolution of PCM during charge and discharge process
Chapter 4 51
Fig. 4.9 shows the phase change evolution of the PCM during charge (a,c,e) and discharge (b,d,f)
processes. The figures show a cross section of the TES in which the inner tube is on the left side
while the wall (Case 1) or the outer tube (Case 2-3) are on the right side. The red area represents
the solid phase of the PCM material, the blue area represents the liquid phase. It can be observed
that the solid-liquid interface moves in different time steps depending on the different geometrical
configurations. It is evident that Case 2 and Case 3 have a more homogeneous heat transfer rate
with respect to Case 1. After 80 min (see also figure 4.8), the solid-liquid interface starts to form
at the top of the TES, where the HTF enters and along the entire length of the inner tube (Case 1)
and of the inner and outer tubes (Cases 2-3). Fig. 4.9e shows that for this time step a film of liquid
PCM starts to form also around the fins. After 200 min it is possible to note the different
characteristics of the solid-liquid interface for the three cases on account of their different
configurations. In Case 1 the solid-liquid interface moves parallel and radially from the centre to
the peripheral wall. On the top of the TES device it is possible to observe a larger area of liquid
PCM, owing to the proximity of the HTF inlet, while a smaller area appears on the bottom. In
Case 2 the interface assumes a kind of monotonic shape (Fig 4.9c,d), while in Case 3 various cells
with liquid PCM form during the process (Fig. 4.9e,f). In Case 1, after 460 min of charge, a large
area of solid material can still be seen (Fig. 4.9a) while, in Case 2 only a narrow portion in the
mid part of TES device remains in solid phase (Fig. 4.9c). For Case 3, the solid PCM forms small
spots into the cells between the fins (Fig. 4.9e). A similar behaviour can be seen for the discharge
phase, but the time to reach complete melting is lower with respect to the charge phase.
(a) (b)
Fig. 4.10 - Melting Fraction for charge (a) and discharge (b) processes.
Figure (4.10) presents the PCM melted fraction versus time for the charge (a) and discharge (b)
processes. This parameter is defined as the volume of PCM in liquid phase divided by the total
volume occupied by the PCM. By definition, the melted fraction is 0 at the beginning of the
charge process and 1 at the beginning of the discharge process. As mentioned, the lowest melting
and solidification time was obtained for Case 3. Moreover, it is evident that Case 1 does not reach
complete melting and solidification after 12 and 8 hours of charge and discharge respectively. The
52 Chapter 4
dashed line again refers to the condition where Case 1 continues for 12 hours as for the charge
phase. For Cases 2-3, in the charge phase the melting fraction is equal to 1 after about 9-10 hours
and the whole PCM is in the liquid phase. At the same time, for Case 1 the melted fraction is
between 0,80-0,84. In the discharge phase, after about 5 hours the melting process is complete for
Cases 2-3, while at the same time the value of the melting fraction is about 0.40 for Case 1.
All these considerations will be better in-depth in the following paragraphs where the comparison
between the two approaches is presented.
Furthermore, the effect of the number of fins on the melting rate was investigated comparing five
different cases. Case A is the reference case and it corresponds to the triplex heat exchanger
without fins already discussed in the previous paragraphs. The number of fins of the others cases
are reported in table 4.5.
The results previously presented in Figures 4.10(a,b) show that the fins influence the melting
fraction especially in the charge phase (fig.4.10a) where the difference between the Case 2 and 3
is considerable, while for the discharge phase this difference is not appreciable. Thus, this
comparative analysis was carried out only for charge process. The melting time is expressed as a
percentage of total time with respect to the case without fins (Case A).
Table 4.5 - Number of fins and melting times for five different cases analyzed
Case A Case B Case C Case D Case E
Number of fins 0 2 4 6 8
Melting Time [min] 440 426 394 372 358
Melting Time % 100 96.8 89.6 84.6 81.4
ΔMT % - -3.2 -7.2 -5 -3.2
Chapter 4 53
Figure 4.11 shows the effect of the number of fins in the melting fraction for the tested cases. It
can be seen that the melting time of PCM decreases increasing the number of fins. Taking as
reference the 85% of the total melting fraction, the melting times were evaluated with respect to
the TTHX without fin (Case A). The complete melting time for Cases B, C, D and E were
respectively as reported in table 4.5.
A significant influence of the number of fins on the melting fraction was founded. The greater the
fins number, the lower the melting time, since, obviously, the fins extend the heat transfer area
and increase the heat transfer rate between the inner tube and the PCM.
Fig. 4.11 - Number of fins effect to the melting time
A reduction of 18.6% was found between the Case A and Case E. The 85% of melting for Case A
was reached in 440 min (7.3 h), thus the addition of 8 finned surfaces inside the storage system
involves a decrease of the melting time for the same percentage equal to 82 min (1.4 h).
The relative percentage difference of melting time ΔMT% increases for Case B and C, while for
Case D ad E decreases. A maximum value of -7.2% is achieved for Case C (four fins) whereby,
the relative improvement decrease with increasing the fins number. In fact, on the one hand the
fins increased heat transfer rate by increasing the total surface area available for heat transfer by
conduction, on the other hand high number of fins reduces the formation of convective cells
decreasing the amount of heat transfer by convection.
It can be concluded that the number of fins has a significant effect on the PCM melting process
that it must be takes into account using finned surface.
In future works, an optimization with respect to the number, the distance, the thickness, the length
and the shape of the fins will be carried out, as well as the effects of different flow rate and fins
number on the TES thermal performance will be studied.
54 Chapter 4
4.5 Validation of the 2D axysimmetric model: comparison
between the two approaches
4.5.1 Material and method
In order to evaluate which of the two proposed approaches shows more accuracy during charge
and discharge processes, a comparison with the results obtained by experimental tests was
performed. Experimental tests were carried out in the laboratories of the research center GREA
Innovació Concurrent (University of Lleida, Spain) on a small scale heat exchanger used as TES
device [60].
Fig. 4.12 - Double tube heat exchanger with fins (a), geometric configuration of TES
system implemented in COMSOL Multiphysics (b).
The TES device is based on the configuration of double pipe heat exchanger with 13 radial copper
fins. The inner tube is copper while the outer is made of transparent material (methacrylate), that
allows a direct view of the phase transition process. Figure 4.12 shows a picture of the TES (a)
and the geometric configuration implemented in COMSOL Multiphysics (b). The geometrical
characteristics of the TES are shown in Table 4.6.
Table 4.6 - Geometrical characteristics of storage system
Units Value
External diameter HTF tube m 0.012
Height m 0.26
Width HTF tube m 0.002
External diameter PCM tube m 0.065
Width PCM tube m 0.006
Number of fins - 12
Diameter fins m 0.052
Chapter 4 55
Width fins m 0.0015
Heat transfer area m2 0.065
PCM mass kg 0.5
Commercial paraffin RT35 from Rubitherm® Technologies GmbH was used as PCM filling the
external tube of the heat exchanger and water circulates through the internal tube as heat transfer
fluid. The main physical properties of this PCM [61] [62] are shown in Table 4.7.
The potential applications in the operative temperature range (35-40 °C) of this type of TES are
related to small-sized systems, such as telecommunication devices or home appliances, for
making them more energy efficient.
Table 4.7 - Properties of Rubitherm RT35
Solid Liquid
Density (kg/m3) 880 760
Specific heat (kJ/kgK) 1.800 2.400
Thermal conductivity (W/mK)
Phase change temperature
Latent heat
0.2 0.2
35°C
157 kJ/kg
Fig. 4.13 shows a schematic diagram of the experimental set-up. The set-up consists of a
thermostatic bath HUBER K25 that controls water inlet temperature, a water pump WILO and a
series of valves to control water flow rate, a digital flow meter Badger Metter Prime Advanced
(range of 0.85–17 l/min, accuracy of 0.25% for velocities below 5 m/s and 1.25% for higher
values) and a system for temperature measurements based on Pt100 DIN-B probes. Both
temperature and flow rate readings are collected in a computer via the data acquisition system
STEP DL01-CPU.
Fig. 4.13 - Diagram of experimental set-up
56 Chapter 4
Working conditions were chosen to achieve temperature gradients of 25 and 15 °C between water
inlet and PCM melting point during charge and discharge respectively. The charge phase was
performed using two volumetric flow rate values in order to have laminar and turbulent regimes,
while the discharge phase was carried out by means of the larger volumetric flow rate value for
both experiments. In all cases, the HTF enters from the upper side of the TES. The specific
conditions used in the experiments are presented in Table 4.8.
Table 4.8 - Summary of charging and discharging experiments carried out.
Experiment 1 Experiment 2
Charge Discharge Charge Discharge
Volumetric flow rate (m3/h) 0.03 0.4 0.4 0.4
Reynolds Number 1600 22000 22000 22000
HTF temperature (°C) 60 20 60 20
A 2D axisymmetric numerical model using both approaches was developed with the COMSOL
Multiphysics platform to simulate the heat exchanger during the phase change processes. The
equations used to model the PCM behaviour are described in the paragraph 4.3 for the first
approach and in paragraph 4.4 for the second approach.
The discharge of experiment 1 and the entire process of experiment 2 are characterized by
turbulent flow in HTF domain. Considering turbulent flow, Reynolds-averaged Navier-Stokes
(RANS) equations were considered the model. The use of RANS equations involves a refined
mesh specially at the boundary layer in order to allow the model to predict the transition from
laminar to turbulent flow. In this case, the mesh adopted for both laminar and turbulent flow was
chosen extremely fine (Fig. 4.19), thus no further mesh refinement was necessary.
The particular RANS model used in this study was the k-ε model. This model is suitable for
incompressible flows, and compressible flows at low Mach number (typically less than 0.3). The
equations solved by the k-ε method are the continuity equation (4.15) and the momentum
equation (4.16). The model introduces two additional transport equations and two dependent
variables: the turbulent kinetic energy, k (Eq. 4.22), that determines the energy of the turbulence
and the turbulent dissipation rate, ε (Eq. 4.23) that determines the scale of the turbulence. The
turbulent viscosity is modeled as given by Equation 4.21:
𝜇𝑇 = 𝜌𝐶𝜇𝑘2
휀 (4.21)
𝜌𝜕𝑘
𝜕𝑡+ 𝜌𝑢 ∙ ∇𝑘 = ∇ ∙ ((𝜇 +
𝜇𝑇𝜎𝑘) ∇k) + 𝑃𝑘 − 𝜌휀 (4.22)
𝜌𝜕휀
𝜕𝑡+ 𝜌𝑢 ∙ ∇휀 = ∇ ∙ ((𝜇 +
𝜇𝑇𝜎𝜀) ∇ε) + 𝐶𝜀1
휀
𝑘𝑃𝑘 − 𝐶𝜀2𝜌
휀2
𝑘 (4.23)
Chapter 4 57
where
𝑢 is the velocity vector [m/s]
𝜌 is density [kg/m3]
𝑃 is pressure [Pa]
𝜇 is the dynamic viscosity [Pa∙s]
𝜇𝑇 is the turbulent (or eddy) viscosity
𝐶𝜇 , 𝐶𝜀1, 𝐶𝜀2, 𝜎𝑘 , 𝜎𝜀 are dimensionless model constants [63] [64]
휀 is the turbulence dissipation rate
𝑘 is the turbulence kinetic energy
𝑡 is the time [s]
Table 4.9. - Value of Rans model costants [63] [64]
Constant Value
𝐂𝛍 0.09
𝐂𝛆𝟏 1.44
𝐂𝛆𝟐 1.92
𝛔𝐤 1.0
𝛔𝛆 1.3
The production term 𝑃𝑘 is given by Equation 4.24:
𝑃𝑘 = 𝜇𝑇 (∇𝑢: (∇𝑢 + (∇𝑢)𝑇) −
2
3(∇ ∙ 𝑢)2) −
2
3𝜌𝑘∇ ∙ 𝑢 (4.24)
4.5.2 Results and discussion
The comparison between the experimental results and the two discussed approaches was carried
out. Figure 4.14 shows the PCM temperature profiles for charge (a) and discharge (b) process. As
said before, two experiments were performed using different volumetric flow rate values. Red
curves represent the first approach, that is the method in which heat transfer by only conduction is
considered. Blue curves represent the second approach, that is the method in which heat transfer
by both conduction and natural convection is considered. The time of the charge process for the
two experiments was imposed equal to 900 and 1600 seconds respectively, while the time of
discharge process was imposed equal to 2100 seconds for both the experiments. The temperature
measurement was taken in a centered position in the PCM domain, near the outer wall in the
radial direction and half way between inlet and outlet in the axial direction.
58 Chapter 4
(a) (b)
Fig. 4.14 - PCM temperature profile for charge (a) and discharge (b) processes.
It is possible to note that the second approach is more accurate because it is closer to the
experimental results. Fig. 4.14a shows that at the beginning of the charge process, up to 800 and
400 seconds for experiment 1 and 2 respectively, both approaches demonstrate good accuracy
with respect to the experimental results. After, the second approach presents approximately the
same temperature values of the experimental results while the first approach differs of about 2-3
°C even if it maintains the same trend. Conversely, during discharge (Fig. 4.14b) the numerical
predictions of both approaches appear very close to the experimental results. This can be
explained by the different nature of the heat transfer phenomena that take place during melting or
solidification. In the case of solidification, conduction is the only heat transfer mechanism, while
in the case of melting, natural convection occurs in the melt layer dominating the heat transfer
process and this generally increases the heat transfer rate compared to the solidification process.
The following figures present the PCM melted fraction versus time for the charge (Fig. 4.15a) and
discharge (Fig. 4.15b) processes. As said before, this parameter is defined as the volume of PCM
in liquid phase divided by the total volume occupied by the PCM and it can assume values
between 0 (only solid PCM) and 1 (only liquid PCM).
Chapter 4 59
(a) (b)
Fig. 4.15 - Melting process for experiment 1 (a) and experiment 2 (b) during charge process
At 1600 second, the value of melting fraction for experiment 1 (Fig. 4.15a) during charge is
approximately 0.8 and 0.94 for the first and second approach respectively. For experiment 2, at
the end of charge (900 seconds) this value is about 0.7 and 0.9 for the first and second approach
respectively (Fig.4.15b). At the end of discharge phase (2100 seconds) the melting fraction
reaches the value of about 0.2 and 0.16 for the first and second approach respectively (Fig.4.16).
It is clearly seen that for the charge process, the difference between the two approaches is
considerable because during melting the heat transfer is strongly influenced by convection, while
for discharge the two curves are very similar, because during solidification the heat transfer is
dominated by conduction.
Fig. 4.16 - Melting fraction for both approaches during discharge process
60 Chapter 4
This is also evident in figure 4.17 that presents the phase change evolution of the PCM for both
experiments and both approaches during charge and discharge processes. The figures show a
cross section of the TES in which the inner tube is on the left side while the wall are on the right
side. The red area represents the solid phase of the PCM material, the blue area represents the
liquid phase.
Exp. 1, First Approach - Charge (a) Exp. 1, Second Approach - Charge (b)
250 s 800 s 1600 s 250 s 800 s 1600 s
Exp. 2, First Approach - Charge (c) Exp. 2, Second Approach - Charge (d)
250 s 450 s 900 s 250 s 450 s 900 s
Chapter 4 61
First Approach - Discharge (e) Second Approach - Discharge (f)
250 s 1050 s 2100 s 250 s 1050 s 2100 s
Fig. 4.17 - Phase evolution of PCM for both experiments and for both approaches during charge
and discharge process
At the beginning of both charging and discharging processes, the solid-liquid interface starts to
form at the top of the TES, where the HTF enters, along the entire length of the inner tube and
around the fins. It is found that natural convection in the melt region as well as heat conduction in
the solid region considerably influence the interface shape and motion during both the melting
and solidification processes. Figures 4.17a,b show the phase evolution of PCM during charge for
experiment 1 (flow rate equal to 0.03 m3/h) for first approach (Fig. 4.17a) and second approach
(fig. 4.17b). At the beginning, the process is dominated by conduction. The solid-liquid interface
moves almost parallel to the heating surface (the inner tube), then when the liquid phase
increases, the influence of natural convection become much strong. After 800 seconds, convection
heat transfer has a higher contribution in melting and helps in increasing the heat transfer rate
within the PCM domain with respect to only conduction. In fact, it is evident that PCM reaches
almost complete melting after 1600 second of charge while with the first approach there is still a
solid PCM fraction near the outer tube. A similar behaviour can be seen for the charge phase of
experiment 2. As an example, figure 4.18 presents the amplitude and direction of the velocity
inside the liquid PCM (red arrows) at 600 seconds for experiment 1. The blue line now shows the
solid-liquid interface. As expected, it can be seen that when the liquid PCM touches a hot surface
of the inner tube, buoyancy forces carries it upward, while when it touches a cooler surface of the
solid PCM or of the outer tube it moves downward forming convective cells.
For discharge phase (fig. 4.17e,f), the two approaches present very similar results. After 2100
seconds the solid-liquid interface is approximately in the same position for both cases. In fact,
during discharge conduction dominates the heat transfer process, thus the influence of natural
62 Chapter 4
convection is very low. Furthermore, finned surfaces enhance the internal heat transfer of a phase
change storage, thus the presence of the fins improves heat transfer by conduction further
reducing the contribution of convection. The nearer the fins, the lower the effect of natural
convection when conduction takes place as the leading heat transfer mode in a solidification
process. Whereby, as said in paragraph 4.4.3, the presence of the fins has a great influence on the
phase change process.
Fig. 4.18 - Convection cells within PCM during melting process at 800s for experiment 1
Heat transfer mode also influences the shape of the solid-liquid interface. In the first approach, in
which only heat transfer by conduction was considered, the solid-liquid interface moves parallel
from the centre to the wall of outer tube. Instead, in the second approach, in which heat transfer
by conduction and natural convection were considered, this boundary is not parallel with the inner
tube but it curves gradually from the top, inward during melting (Fig. 4.17b,d) and outward
during solidification (Fig. 4.17f). In fact, the presence of gravity, heterogeneous temperature field
and heterogeneous density generate buoyancy force in liquid PCM domain which allows the
formation of this particular shape of the solid-liquid interface.
As said before, the second approach is more accurate because it is closer to the experimental
results. However, it is important to compare the required computation times and the mesh for the
two proposed approaches.
Table 4.9 - Summary of the model simulations to compare the two approaches studied.
First Approach Second Approach
Charge
Exp. 1
Charge
Exp. 2
Discharge
Exp. 1-2
Charge
Exp. 1
Charge
Exp. 2
Discharge
Exp. 1-2
Duration of
simulation (real time) 22 h 10.8 h 5.5 h 156.1 h 80.8 h 56.4 h
Physical time
(simulation time) 1600 s 900 s 2100 s 1600 s 900 s 2100 s
Chapter 4 63
Table 4.9 shows that the time elapsed during the execution of the simulations for the second
approach are 7 and 10 times greater than those related to the first approach for charge and
discharge processes respectively. In fact, 22 hours were required to complete the first experiment
using the first approach, while 156.1 hours were required to complete the same experiment using
the second approach. The computation is performed on a ASUS workstation with I7 Quad-Core
CPU and 16 GB memory. Basically, this difference depends on the increasing complexity due to
solve the continuity (15), momentum equations (16) and buoyancy forces used to simulate the
behaviour of the PCM in liquid phase. In fact a finer mesh was required using the second
approach and consequently more computation time was needed.
(a) (b)
Fig. 4.19 - Free triangular mesh used for first approach (a) and second approach (b)
For all models, a free triangular mesh geometry was selected using 63252 elements and 3428
boundary elements for the first approach (Fig.4.19a), while 255687 elements and 7824 boundary
elements for the second approach (Fig. 4.19b).
4.6 Conclusions
Numerical study of latent heat thermal energy storage device were presented in chapter 4, using
2D and 3D numerical simulation codes specifically implemented in the COMSOL Multiphysics
environment. Two different approaches were analyzed to perform the behavior of PCM during
phase transition. The first approach considers heat transfer only by conduction in both solid and
liquid PCM phases. The second approach considers heat transfer by conduction and natural
convection in liquid PCM domain. To model the phase transition, the apparent heat capacity
formulation was used in both approaches. In this method, the latent heat is implemented by
increasing the heat capacity of the material, while the phase change process is modelled by
assuming that the transition takes place in a narrow range of temperature rather than at a fixed
temperature.
64 Chapter 4
A 3D numerical simulation code was presented in paragraph 4.3 and developed to analyze
behaviour and performance of a thermal energy storage systems with phase change materials
using the first approach, i.e. heat transfer only by conduction in PCM liquid domain was
considered. The configuration of shell and tube heat exchanger was selected to design the TES
and Hydroquinone was used as PCM. This configuration has been chosen for the storage device
that will be implemented in the laboratories for TES technologies of the DIMCM-University of
Cagliari. The heat exchange between the HTF and PCM simulating the phase transition, but also
the fluid dynamics of the HTF inside the tubes of the storage system was carefully studied and
evaluated. The configuration of the storage system has led to an uniform distribution of the heat
flow across the surface of the tank. The results obtained show that the complete transition was
reached in about 2 hour for charging process and 1 hour for discharging process. On the other
hand, the PCM nearest to the shell was the last that undergoes the transition in both charge and
discharge phases. With the first approach, the convection and the buoyancy force in liquid PCM
domain were not considered, so the solid-liquid interface moves around the tubes uniformly. The
shape of this boundary and the melting and solidification time depend on the heat transfer process
considered.
In paragraph 4.4, a 2D axysimmetric numerical model based on the second approach was
presented. Three different geometrical configuration of a TES system were studied and compared
to identify the best solution as regards thermal energy storage with PCM materials. A double tube
(Case 1), a triplex (Case 2) and a triplex with circular fins (Case 3) were analyzed to evaluate
temperature and phase distribution in both charge and discharge phases. It was found that the
different configurations of the three systems considered had a strong impact on the performance
of the phase change process. In Case 1 the solid-liquid interface moved parallel and radially from
the centre to the wall of the TES. In Case 2 the interface assumed a monotonic shape, while in
Case 3 various cells with liquid PCM formed during the process. As expected, the triplex heat
exchanger (Cases 2 and 3) were the solutions that allowed the faster response of the TES device
during the charge and discharge processes. The insertion of fins (Case 3) allowed, in particular,
not only an increase in the heat exchange surface of the inner HTF tube, but also the creation of
cells in the PCM volume that determined faster melting/solidification of the PCM. A time of 12
and 8 hours was considered as a reference period for charge and discharge respectively. In this
period, complete melting and solidification of the PCM was achieved only in Cases 2 and 3. A
melted fraction for both phases was analyzed. For charge process, a complete melting was
achieved in about 9-10 hours in Cases 2 and 3, while a value of about 80-84% of PCM liquid
fraction was reached in Case 1 in the same time interval. For discharge process, a complete
solidification was achieved in about 4 hours in Cases 2-3, while a value of about 40% of PCM
solid fraction was reached in Case 1. The second approach was used in this model, thus heat
transfer by both conduction and natural convection was calculated in PCM domain. The role of
natural convection involves not only the heat transfer rate during melting process but also the
shape of the solid-liquid interface. In fact, using the first approach the solid-liquid interface moves
uniformly around the tubes while, the second approach takes into account the buoyancy forces
that modify the shape of the interface.
Furthermore, the effect of the number of fins on the melting rate was investigated comparing five
different cases (0, 2, 4, 6, 8 fins). A big influence of the fins number on reducing the melting time
was found. Considering the 85% of total melting, a reduction of 18.6% of melting time was
estimated for the case with 8 fins with respect to the case without fins. The relative percentage
difference of melting time ΔMT% presents a maximum value of -7.2% for TES with four fins,
while for higher number of fins this parameter decreases. Whereby, on the one hand the fins
Chapter 4 65
increased heat transfer rate by increasing the total surface area available for heat transfer by
conduction, on the other hand high number of fins reduces the formation of convective cells
decreasing the amount of heat transfer by convection.
In paragraph 4.5, the validation of the two proposed approaches was carried out through a
comparison with the results obtained by experimental tests. The transient behaviour of a LHTES
system based on the configuration of a finned double tube heat exchanger filled with paraffin
RT35 as PCM was investigated. The first approach takes into account the heat transfer only by
conduction in liquid PCM domain. The second approach takes into account the heat transfer by
heat conduction and natural convection in liquid PCM domain and also, the Boussinesq
approximation was introduced to consider the buoyancy forces. In order to evaluate which one of
the two proposed approaches show more accuracy during charge and discharge processes, a
comparison with the results obtained with two experimental tests was carried out. These tests
were performed in the laboratories of the research center GREA Innovació Concurrent
(University of Lleida, Spain). Overall, a good agreement with the experimental temperature
profiles during charge and discharge phase was obtained. However, it was found that heat transfer
mode influences the interface shape and motion during both the melting and solidification
processes. In fact, natural convection in melt region drives and improves the heat transfer rate
increasing the velocity of the solid-liquid interface. A time of 1600 and 900 seconds was
considered as a reference period for the charge phase of experiment 1 and 2 respectively, while a
time of 2100 seconds was considered for discharge phase of both experiments. At the end of
charge phase, the temperature profile obtained with the second approach shows a good agreement
with respect to the experimental results, while the first approach is less accurate. Instead, the
numerical prediction of both approaches appears very similar to the experimental results during
discharge process. A melted fraction for both phases was analyzed. For experiment 1, melting
fraction values of 0.8 and 0.94 were reached at the end of charge for first and second approach
respectively, while for experiment 2, melting fraction values of 0.7 and 0.9 were reached at the
end of charge for first and second approach respectively. At the end of discharge, melting fraction
values of 0.16 and 0.2 were obtained for first and second approach respectively for both
experiments. These differences can be explained considering that the different nature of the heat
transfer phenomena that take place when a PCM melts or solidifies. During charge the difference
between the two approaches, evenly considering the temperature profile or the melting fraction, is
high because in melting process the heat transfer is dominated by convection, while during the
discharge the results are very similar, because in solidification process the heat transfer is
dominated by conduction. Furthermore it was found that the two approaches had a strong impact
on the shape of the solid-liquid interface. In the first approach solid-liquid interface moves
parallel and radially from the centre to the wall of the TES, while in the second approach, natural
convection and buoyancy force this boundary slopes gradually from the top, inward during
melting and outward during solidification. Finally, first approach was simple and required
relatively low computational resources but it has proven less accurate. A good fitting was
obtained using the second approach that was more closer to the experimental results thus, natural
convection plays a significant role in phase change process and it must be taken into account. The
effects of natural convection on the shape and the motion of solid-liquid interface can not be
neglected. However, it must be considered that the addition of natural convection implies a major
requirement of computational resources.
66 Chapter 5
Chapter 5
Project design and implementation of a
TES test rig
5.1 Introduction
The project, design and implementation of a test rig was carried out to investigate thermal energy
storage systems within the laboratory for TES technologies of the Department of Mechanical,
Chemical and Material of the University of Cagliari. In particular an accurate selection of test rig
components was specifically chosen for experimental investigation of latent heat thermal storage
devices.
The experimental facility was designed not only to be an important tool for the research activity in
order to validate the developed numerical models, but also for the experimental investigation
applied to medium-high temperature industrial processes. For these reasons, a PCM-TES
prototype was specially designed and build as latent heat thermal energy storage device based on
the configuration of shell and tube heat exchanger. D-Mannitol was selected as PCM material
while silicone oil Syltherm 800 was selected as HTF. D-Mannitol and Syltherm 800 were already
presented in chapter 4. The operating parameters of the test rig are reported in table 5.1:
Table 5.1 - Operating parameters of the test rig
Temperature Max 350 °C
Pressure Max 15 bar
Nominal pressure 12 bar
HTF Flow-rate [min- Max] 0.5-3 m3/h
At the time of writing the test rig is already build while the storage system is still under
construction.
5.2 Design and implementation of the LHTES test rig
The test rig consists of the following components as reported in figure 5.1:
A. Electric heater
B. Air cooler
C. Latent heat thermal energy storage device
Chapter 5 67
D. Fluid Circulation Pump
E. Thermal Fluid Expansion Tank
F. Pump empty/full
G. Air Separation Unit
The pump circulates the HTF within the plant during the charging and discharging processes.
During charge, the HTF is heated by the electric boiler until the operating temperature conditions.
Then it enters the TES system releasing thermal energy to the PCM. A valves by-pass system
allows to the continuous recirculation of the HTF avoiding to passing into the air cooler. During
discharge, cold HTF enters the TES absorbing the thermal energy accumulated by the PCM, then
it flows into the air cooler considered as the thermal user.
Fig. 0.1 - Test rig layout
Figure 5.1 shows the test rig layout. HTF temperature and pressure are measured in different
sections of the facility by temperature (indentified with T in figure 5.1) and pressure (identified
with PT in figure 5.1) sensors.
The pump circulates the HTF within the plant during both charge and discharge processes. Two
shut-off valves, located one before and one after the pump, allow to isolate the pump when it is
necessary (e.g. for maintenance). Then the HTF is heated up to the operating conditions inside the
electric boiler.
A servo-actuated valve (identified with VSA in Figure 5.1) located at the exit of the boiler allows
to control the HTF flow rate that circulates in the "storage pipes" (it consist of TES and aircooler)
or "skid pipes" (it only consist of heater and pump) admitting three operating conditions:
Valve fully closed (0%): full HTF flow rate is available to the TES and the thermal user
(the aircooler).
68 Chapter 5
Valve fully open (100%): full HTF flow rate is not available to the TES and the thermal
user but it is recirculated inside the heater skid.
Valve partially open (x%): part of HTF flow rate flows to the TES, part of the HTF
recirculates inside the skid.
Figure 5.2 shows the valves system used to modify the direction of the HTF at the inlet of the
TES. In fact, this system allows two different HTF inlet direction modes (figure 5.3a,b): in the
first, the HTF enters from the top of the storage system while in the second, the HTF enters from
the bottom.
Fig. 5.2 - Valves system to modify the direction of the HTF at the inlet of the TES
The first mode is achieved by closing of valves 1 and 2 and opening of valves 3 and 4 (fig. 5.2).
In this condition the HTF enters the TES from the upper part as reported in figure 5.3a. The
second mode is achieved by opening valves 1 and 2 and closing valves 3 and 4 (fig. 5.2). In this
condition the HTF enters the TES from the bottom as reported in figure 5.3b.
Chapter 5 69
(a) (b)
Fig. 5.3 - Two different modes concerning the HTF direction at TES inlet
This valves system is implemented to study the thermal performance of the storage device in
function of the direction of HTF inlet. Furthermore it allows to analyze all the cases in which
partial load conditions occur. In fact, it is not always possible to complete full charging and
discharging processes for example, in cases of heater failure, when thermal energy is suddenly
required or to fulfil peak-load during time. This system allows to avoid the formation of different
solid-liquid interfaces which move in different directions inside the PCM. Not homogeneous
phase transition process and different temperature profile are possible due to the presence of
multiple melting/solidification fronts inside the PCM resulting loss thermal energy.
In the following paragraphs the main components of the test rig will be presented and analyzed.
5.2.1 Skid
A skid from "Pirobloc S.A." was selected for moving and heating the HTF. Figure 5.4 shows the
skyd implemented in the laboratory.
To thermal
user
From heater
To thermal
user
From heater
70 Chapter 5
Fig. 5.4 - Skid of the test rig
The skid is composed of the following main elements:
Electric heater
The heater body is made of carbon steel with barrelled bottoms. The size of the heater body are
2645 mm (length) x 1450 mm (height) x 420 mm (depth), with a total capacity of 45 liters. The
maximum operating temperature and pressure are 350 °C ad 15 bar respectively. The electrical
resistance is made of AISI-316 stainless steel, and generates a maximum power equals to 41 kW.
This power can be adjusted from 0 to 100%. This element has low density heating which means
that the heat produced per surface area is very low (3.15 W/cm²) in order to avoid the oil
cracking.
Control panel
Processes control is carried out by the PLC model S7-1200 system from Siemens. Temperature
and pressure measured with transducers placed in the boiler and in different section of the plant
(fig. 5.1) are the input of the PLC. Two inverters allow the variation of rotational speed of the
pump and of the air cooler fan. Furthermore a servo-actuated valve, controlled by the panel,
allows to adjust the flow rate that circulates in the plant.
The control devices placed into the skid are:
1 Transmitter for differential pressure.
1 Transmitter for maximum pressure (minimum flow control).
2 Pressure gauges Ø 100, of 0-25 kg/cm2, with glycerine bath and with its own
expansion.
Quadrants and closure taps.
Chapter 5 71
3 Temperature probes type PT-100 (T1 for inlet temperature, T2 for outlet
temperature, T3 as safety outlet temperature in figure 5.1 respectively).
3 Thermowells for the placement of the probes.
Circulating pump
A nominal flow rate of 12 m3/h is set on the circulating pump model "ALLWEILER CTWH-32-
160". The pump is designed to work with thermal oil with maximum temperature and pressure of
400 °C and 15 bar respectively. The pump has a nominal rotational speed equal to 2900 rpm and
the presence of an inverter allows to vary the pump velocity. Fig. 5.5 reports the pump
characteristic and system curves.
Fig. 5.5 - Pump characteristic and system curves
Expansion tank
An expansion tank is a metal tank used to accommodate fluctuations in the volume the entire
system. These fluctuations occur because HTF expands in volume during heating and reduces
volume during cooling. This tank has a capacity of 400 liters and it is equipped with a magnetic
level indicator. Nitrogen is used to pressurized the tank.
72 Chapter 5
5.2.2 Air cooler
The air cooler producted by "Pirobloc S.A." (Fig. 5.6) allows to cool the HTF during the
discharge phase in order to simulate thermal demand of an user.
Fig. 5.6 - Air cooler placed outside the laboratory
It consists of 36 helical finned tubes arranged in two rows of 18 tubes each, made of carbon steel
ASTM A106 GrB (diameter of 25.4 mm, and length of 1000 mm). The air cooler is designed for a
maximum temperature and pressure of 410 °C and 15 bar respectively.
Chapter 5 73
Fig. 5.7 - Scheme of air cooler
Figure 5.7 reports the scheme of the air cooler. The HTF flows into the tubes while air flowing
outside is forced by a fan driven by an electric motor whose rotational speed can be varied by
inverter. The HTF outlet temperature is measured by a temperature transmitter type PT-100
connected with the control system.
5.2.3 Air Separation Unit
Air trapped in the system can produce major problems such as reduced heat transfer, loss of
system efficiency, pipe corrosion, pump damage and increased energy consumption. The air
separator unit consists of a tube portion with a larger diameter than the other tubes forming the
piping, which allow to aerate the HTF by flowing the gases directly to the expansion tank.
5.2.4 Thermal energy storage device
The design project of thermal energy storage device specifically applied to latent heat
technologies was carried out. The geometry of the system is based on a configuration of shell and
tube heat exchanger whose shell is filled with PCM while the HTF flows in the tube side.
Different TES geometrical configuration were proposed and studied during last years as reported
by Sharma [6] and Farid [12]. Numerous researcher suggested the configuration of shell and tube
heat exchanger as the most suitable for latent applications. Buddhi [65] designed and fabricated a
PCM based shell and tube type heat exchanger without fins for low temperature industrial waste
heat recovery. Trp et al. [66] analysed numerically and experimentally the transient phenomenon
during both charging and discharging processes of the shell and tube latent energy storage system
using paraffin as PCM. Adine and Qarnia [37] presented a numerical analysis of the thermal
behaviour of a shell-and-tube PCM system comparing the utilization between one and two PCM.
Cabeza et al. [9] conducted an experimental analysis of a shell and tube heat exchanger applied to
74 Chapter 5
solar cooling. Morcos [67] studied an experimental investigation of a shell-and-tube heat
exchanger concept for the use in a latent heat thermal energy storage system for solar heating
applications. Hosseini et al. [68] investigated the thermal behaviour of phase change material
(PCM) inside a shell and tube heat exchanger. Agyenim et al. [69][70] investigated melting and
solidification on a paraffin in a shell and tube heat exchanger for various operating conditions and
geometric parameters.
For the specific application the classical configuration of this type of heat exchanger was
modified to adapt the shell side to the storage of the PCM material. Figure 5.9 shows the TES
system layout which consists of a vessel with a tube bundle inside. This bundle is composed of 32
tubes distributed in square pitch as shown in figure 5.9b.
The tube bundle, was designed to operate at a maximum temperature and pressure of 370 °C and
16 bar respectively, while the shell was designed to operate at a maximum temperature and
pressure of 370 °C and 1.49 bar respectively. Both tube bundle and shell are made of stainless
steel.
The HTF flows in the tube side while PCM material is placed in the shell side. Two inclined
nozzles DN-80 ( identified with J in Figure 5.9a) were implemented in the upper part of the TES
in order to facilitate the introduction of the PCM in the shell side during the filling procedure. A
further nozzle DN-60 (identified with K in Figure 5.9a) coupled with gate valve was inserted in
the TES bottom to realize emptying operation.
A particular floating head system was implemented in order to make shell side accessible for
cleaning and inspection. This system allows to withstand the pressure in the shell side and avoids
leakage of PCM during operation.
The geometrical characteristic and the design operative parameters of the TES are obtained using
the design method presented in paragraph 5.2.5, and reported in Table 5.2.
Table 5.2 - Geometrical characteristics and design operating parameters of PCM-TES device
Units Value
Height m 1.5
External Diameter m 0.273
Number of tubes - 32
External diameter tubes m 0.01588 (5/8'')
Pitch m 0.0381
Maximum temperature °C 370
Maximum pressure tube side bar 16
Maximum pressure shell side bar 1.49
Furthermore, considering D-Mannitol as PCM and Syltherm800 as HTF, a preliminary evaluation
of thermal performance was carried out. The operating parameters of TES device are reported in
Table 5.3.
Table 5.3 - Operating parameters of PCM-TES device using D-Mannitol
Chapter 5 75
Units Value
HTF inlet temperature - Discharge °C 100
HTF inlet temperature - Charge °C 180
HTF flow m3/h 0.5
PCM mass kg 90
PCM melting temperature °C 167
PCM latent heat kJ/kg 234
Nominal latent heat storage capacity kWh 5.7
(a) (b)
Fig. 5.9 - TES layout (a) and tube bundle scheme (b)
In order to minimize the heat losses, 100 mm of rock wool (identified with L in Figure 5.6a) were
installed on both lateral walls and two ends.
76 Chapter 5
Square pattern was selected to facilitate the insertion of the temperature measurement system
inside the TES shell side. The temperature measurement system allows to determine the PCM
temperature profiles in both radial and axial direction during operation. In the axial direction,
eight thermocouples (type K) were inserted in order to cover the entire height of the TES, while
thermocouple multipoint sensor systems (type K) were used in radial direction. These systems
were placed in three different section (upper, middle and bottom part) measuring the temperature
evolution from the center to the outer wall of the TES. Finally, two additional thermocouples
were inserted to measure the temperature of the HTF at the TES inlet and outlet.
A numerical model based on the Logarithmic Mean Temperature Difference (LMTD) method
[71] was developed in Matlab environment to determine both the heat transfer area of the storage
device (sizing problem) and the TES performance (rating problem). Even if LMTD method is
used for heat exchanger in which the heat transfer occurs between the two fluids, it can be also
applied for PCM applications [16].
5.2.5 LMTD method
During phase transition, PCM material releases thermal energy through an isothermal
transformation (for pure substance). Figure 5.10(a,b) reports the fluid temperature variation in
heat exchanger when phase transition occurs during charge (a) and discharge (b) processes.
(a) (b)
Fig. 5.10 - Fluid temperature variation in heat exchanger when occurs phase transition during
charge (a) and discharge (b) processes.
In general, in heat exchanger applications, the inlet and outlet temperatures are commonly
specified based on the fluid in the tubes. The temperature change that takes place across the heat
exchanger from the entrance to the exit is not linear. A precise temperature change between two
fluids across the heat exchanger is best represented by the log mean temperature difference:
∆𝑇𝑚𝑙 =∆𝑇2 − ∆𝑇1
ln (∆𝑇2∆𝑇1
)
(5.1)
THTF,1
THTF,2
Tm
Tm
THTF,1
THTF,2
Chapter 5 77
where:
∆𝑇1 = 𝑇ℎ1 − 𝑇𝑐1 (5.2)
∆𝑇2 = 𝑇ℎ2 − 𝑇𝑐2 (5.3)
The variables 𝑇ℎ and 𝑇𝑐 represent the temperature of hot and cold fluids that flow in the heat
exchanger, while the subscripts 1 and 2 refer to the inlet and the outlet conditions. If one of the
two fluids is replaced by a PCM (Fig. 5.10a,b), the heat exchanger becomes a heat storage type.
Indeed, the PCM has not a constant temperature along the heat exchanger and the temperature
will also change with time. Nevertheless, a simplified first approach was used assuming a
constant temperature equal to the phase change temperature along the heat exchanger and
constant with time. Considering that the PCM is everywhere at the phase transition temperature
means that all inlet and outlet temperatures of hot fluid can be replaced by the phase change
temperature 𝑇𝑚. Thus, the Equation 5.1 becomes:
∆𝑇𝑚𝑙 =∆𝑇2 − ∆𝑇1
ln (∆𝑇2∆𝑇1
)=(𝑇𝑚 − 𝑇𝐻𝑇𝐹,2) − (𝑇𝑚 − 𝑇𝐻𝑇𝐹,1)
ln (𝑇𝑚 − 𝑇𝐻𝑇𝐹,2𝑇𝑚 − 𝑇𝐻𝑇𝐹,1
)
(5.4)
The rate of the heat transfer between the two fluids in general, and between PCM and fluid in
particular, is related with the mean logarithmic temperature difference (Eq. 5.4) by the equation:
�̇� = 𝑈 ∙ 𝐴 ∙ ∆𝑇𝑚𝑙 (5.5)
where, �̇� is the heat transfer rate [W], 𝑈𝑑 is the overall heat transfer coefficient [W/m2∙K]
including heat transfer coefficients of the fluids and heat conduction through the heat exchanger
material and 𝐴 is the heat exchanging area [m2].
The clean (a) and dirty (b) overall heat transfer coefficient can be calculated from Equation
5.6(a,b):
𝑈𝑐 =1
1ℎ𝐻𝑇𝐹
+ 𝑅𝑤 +1
ℎ𝑃𝐶𝑀∙𝐴𝑖𝐴𝑜
(5.6a)
𝑈𝑑 =1
𝑈𝑐+ 𝑅𝑓,𝑜 + 𝑅𝑓,𝑖 ∙
𝑑0𝑑𝑖
(5.6b)
78 Chapter 5
where ℎ𝐻𝑇𝐹 and ℎ𝑃𝐶𝑀 are the heat transfer coefficients [W/m2∙K] of HTF and of PCM, 𝑅𝑤 is the
conduction coefficient through the wall [m2∙K/W], 𝑅𝑓,𝑖 and 𝑅𝑓,𝑜 are the fouling factors for the
inner and outer pipe respectively [m2∙K/W], 𝐴𝑖 and 𝐴𝑜 are the inner and the outer surface area of
the tube wall [m] while 𝑑𝑖 and 𝑑𝑜 are the diameter of inner and outer pipe respectively [m].
Convective heat transfer coefficients for HTF
The convective heat transfer coefficient between HTF (inside the tube) and tube walls is a
function of the thermal conductivity of the fluid 𝑘𝐻𝑇𝐹, the internal diameter of the tubes 𝑑𝑖 and
the Nusselt number 𝑁𝑢 as reported in Equation 5.7:
ℎ𝐻𝑇𝐹 =𝑘𝐻𝑇𝐹 ∙ 𝑁𝑢
𝑑𝑖 (5.7)
A correlation for the Nusselt number for laminar flow was provided by Sieder and Tate:
𝑁𝑢 = 1.86 ∙ (𝑅𝑒 ∙ 𝑃𝑟
𝐿𝑑𝑖⁄
)
13⁄
(𝜇𝑜𝑖𝑙𝜇𝑤
)0.14
(5.8)
where 𝐿 is the tubes length, 𝑅𝑒 and 𝑃𝑟 are the Reynolds and Prandtl numbers respectively while
𝜇𝑜𝑖𝑙 and 𝜇𝑤 are the dynamic viscosity of the HTF calculated at bulk fluid average temperature and
at wall average temperature. It attempts to explicitly account for the fact that the viscosity of the
fluid next to the wall is different from that in the bulk at any axial location. If the wall is hot, and
we consider a liquid being heated in the pipe, the viscosity of the wall fluid will be smaller than
that of the fluid in the bulk. This increases the velocity gradient at the wall and therefore the heat
transfer rate compared to that obtained by assuming that the fluid is at a single temperature across
the entire cross-section.
Reynolds and the Prandtl numbers are obtained respectively by the relations:
𝑅𝑒 =𝜌𝐻𝑇𝐹 ∙ 𝑢𝐻𝑇𝐹 ∙ 𝑑𝑖
𝜐𝐻𝑇𝐹 (5.9)
𝑃𝑟 =𝐶𝑝,𝐻𝑇𝐹 ∙ 𝜇𝐻𝑇𝐹
𝑘𝐻𝑇𝐹 (5.10)
Chapter 5 79
The parameters 𝜌𝐻𝑇𝐹, 𝑘𝐻𝑇𝐹, 𝐶𝑝,𝐻𝑇𝐹, are density, thermal conductivity and specific heat of the
HTF while 𝑢𝐻𝑇𝐹 is the HTF velocity inside the tubes.
For a smooth surface and fully turbulent conditions (Re>10.000), the Dittus–Boelter equation is
widely used:
𝑁𝑢 = 0.023 ∙ 𝑅𝑒0.8𝑃𝑟𝑛 (5.11)
where, 𝑛 = 0.4 for heating, and 𝑛 = 0.3 for cooling.
Conductive heat transfer coefficient
The heat transferred from the tubes wall to the PCM, placed outside the tubes, happens by
conduction. The heat transfer coefficient for the wall is given by the equation:
𝑅𝑤 =𝛿𝑤
𝑘𝑤𝐴𝑙𝑚𝐴𝑜
(5.12)
where:
𝛿𝑤 is tube thickness [m]
𝑘𝑤 is tube the thermal conductivity [W/m∙K]
𝐴𝑙𝑚 = (𝐴𝑜 − 𝐴𝑖) ln(𝐴𝑜 𝐴𝑖⁄ )⁄ is the log mean area
𝐴𝑖 = 2𝜋𝐿𝑟𝑖 is the inner surface area of the tube wall [m]
𝐴𝑜 = 2𝜋𝐿𝑟𝑜 is the outer surface area of the tube wall [m]
Fouling factor
After a period of time, the heat transfer surfaces of a heat exchanger may become coated with
deposits from the heat transfer fluids or corrosion. In either case, the additional resistance to heat
transfer due to these materials decreases the performance of the heat exchanger and must be
accounted for. This is done through the use of experimentally determined fouling factors. If the
fouling resistance is not given, it can be adopted values specified in the TEMA (Tubular
Exchanger Manufacturers Associations, www.tema.org) standards. Representative values of
fouling factors are given in Table 5.3 for some common fluids.
80 Chapter 5
Table 5.3 - Representative fouling factors in heat exchangers
Heat transfer coefficient for PCM
Determine the heat transfer coefficient in PCM side is more complicated. This coefficient is
obtained through the equation (43) expressed as a function of the Nusselt number. However,
during the phase change process, the heat transfer mode is not unique but three different regimes
exist. The first regime appears at the beginning of the melting process where the heat transfer
process is dominated only by conduction and is characterized by the relatively large magnitude of
the Nusselt number that decreases as time elapses. The second regime occurs when melting
process becomes more significant as time progresses thus, natural convection dominates the heat
transfer process. Between these two regimes lies the transition regime where both conduction and
convection are prime factors in the heat transfer process.
Many authors proposed experimental correlations to determine the Nusselt number for PCM
during phase transition process. Jesumathy et al. [72] investigated the behaviour of paraffin wax
in cylindrical tube and proposed a correlation in which the Nusselt number is function of Rayleigh
number (obtained by the product between the Grashof and Prandtl numbers 𝑅𝑎 = 𝐺𝑟 ∙ Pr), the
thickness of the PCM material and the length of the storage device. Wang et al. [73] presented an
experimental investigation of the melting process in the vicinity of a heated vertical wall in a flat-
plate heat pipe and proposed a correlation to determine a time average Nusselt number as a
function of Rayleigh number, Prandtl number and the location of the solid-liquid interface.
5.2.6 Design of the TES device
The design procedure of shell and tube heat exchanger [74] applied to latent heat thermal energy
storage was developed in Matlab environmental using the LMDT method. The TES design was
performed in discharge phase using an iterative technique in order to evaluate the best device
configuration to supply a heat thermal load required by user.
At the beginning, the selected operating parameters necessary to design the TES system are:
HTF flow rate (selected in the pump operating range of the test rig)
HTF inlet temperature (selected in the heater operating range of the test rig)
HTF operating pressure (selected in the pump operating range of the test rig)
length of storage device
Chapter 5 81
allowable pressure drop
heat thermal power required by the user.
The main steps of the iterative scheme are summarized as follows:
I. Calculate the required thermophysical properties of HTF and PCM at operating
conditions. As said before, the used HTF is the silicone oil Syltherm800, which required
properties [58], i.e. viscosity, thermal conductivity, density, and specific heat are obtained
in function of bulk temperature, while the selected PCM is the D-Mannitol which
properties are reported in Table 4.3.
II. Perform energy balance and find out the HTF outlet temperature using the Equations
5.13-5.14:
�̇� = ∫ �̇�𝐶𝑝𝑑𝑇 = �̇�𝐶𝑝̅̅ ̅(𝑇𝐻𝑇𝐹,2 − 𝑇𝐻𝑇𝐹,1)𝑇𝐻𝑇𝐹,2
𝑇𝐻𝑇𝐹,1
(5.13)
𝑇𝐻𝑇𝐹,2 =�̇�
�̇�𝐶𝑝̅̅ ̅+ 𝑇𝐻𝑇𝐹,1 (5.14)
Where �̇� is the thermal power required by the user [W], �̇� is the HTF flow rate
[kg/s], 𝐶𝑝̅̅ ̅ is the specific heat [J/kg∙K] evaluated in the temperature range between
𝑇𝐻𝑇𝐹,1 and 𝑇𝐻𝑇𝐹,2. These two temperatures represent the HTF inlet and outlet
temperature [K].
III. Calculate the log mean temperature difference ∆𝑇𝑚𝑙 given by Equation 5.4.
IV. Assume a reasonable value of overall heat transfer coefficient 𝑈𝑜′ for the first process
iteration. The value of 𝑈𝑜′ with respect to operating fluids, can be taken from Table 5.4:
82 Chapter 5
Table 5.4 - Typical overall heat transfer coefficient for shell and tube heat exchangers
Then, evaluate the heat transfer area 𝐴′ required using 𝑈𝑑′ for the first iteration:
𝐴′ =�̇�
𝑈𝑑′ ∙ ∆𝑇𝑚𝑙
(5.15)
V. Fixed the length 𝐿 [m] and the outer diameter of the tubes 𝑑𝑜 [m], evaluate the tubes
number 𝑁𝑡′ required to provide the heat transfer area 𝐴′ through the Equation 5.16.
𝑁𝑡′ =
𝐴′
𝜋 ∙ 𝑑𝑜 ∙ 𝐿 (5.16)
VI. Selecting the tube pitch and the number of passes from Table 5.11 [74], the internal shell
diameter is obtained.
Chapter 5 83
Fig. 5.11 - Tube sheet layout [74]
VII. Determine the heat transfer coefficient for tube ℎ𝐻𝑇𝐹 side using Equations from 43 to 47.
Determine the shell side heat transfer coefficient. As said before, PCM is located in the
shell side and the heat transfer coefficient is obtained by experimental correlations.
Finally evaluate the tube-wall resistance from Equation 4.12.
VIII. Select the fouling factors from Table 5.3.
IX. Calculate overall heat transfer coefficient 𝑈𝑑′′ based on the outside tube area using
Equation 5.6.
X. The iterative method involves the comparison between the obtained value 𝑈𝑑′′ and the
value assumed by the first iterative step 𝑈𝑑′ . If the different between these two values is
less than an imposed error 휀, the storage device is correctly designed, if not it is necessary
repeat the calculations starting from step IV.
XI. Calculate the tube-side pressure drop ∆𝑃𝑡𝑢𝑏𝑒 which consist of the pressure drop caused by
frictional losses evaluated trough the Equation (5.17) and the pressure drop caused by the
presence of curves for heat exchangers with multi-pass (not in this case).
84 Chapter 5
∆𝑃𝑡 = 𝑓𝐷𝜌𝐿
𝑑ℎ
𝑣
2 (5.17)
where 𝑓𝐷 is the friction factor, 𝜌 is the HTF density [kg/m3], 𝐿 is the pipe length [m],
𝑑ℎ = 4𝐴 𝑍⁄ is the mean hydraulic diameter [m], 𝑣 is the flow velocity [m/s], 𝐴 is the
pipe cross section area available for flow [m2] and 𝑍 is the wetted perimeter [m]
XII. Calculate shell side pressure drop ∆𝑃𝑠ℎ𝑒𝑙𝑙: during transition the PCM change its density
and consequently its volume.
Furthermore, two important aspects must be taken into account. First aspect concerns that during
the design calculation a volume % overdesign must be considered. Overdesign represents an extra
volume provided beyond that required to compensate the volume variation of PCM. D-Mannitol
has a volume change of about 10% during solid-liquid transition. Moreover, this extra-volume
takes into account the presence of baffles which further reduce the available volume. The second
aspect concerns that D-Mannitol reacts with oxygen from the atmosphere enclosed in the storage
device causing the change of thermochemical properties of the material and affecting thermal and
cycling stability [75]. Thus, in this specific application, nitrogen is selected to fill the atmosphere
enclosed in the storage device.
It is obvious that this method should be used only for a preliminary analysis because it is based on
several simplified assumptions. In fact, constant conditions on the PCM side are assumed thus,
there is no time dependency in the solution. The simple solution is derived using the
approximation that the one side of the heat exchanger contains PCM that is always at the phase
change temperature. The LMTD relies only on temperatures, not accounting for the energy stored
during a phase change process, since it occurs at almost constant temperature but with important
enthalpy variations. Moreover the solid-liquid front moves during the process, consequently
varying the value of overall heat transfer coefficient. Nevertheless, the solution gives important
insight into the influence of the main design parameters.
At the time of writing the test rig is already build while the storage system is still under
construction. Once implemented the TES device, accurate experimental tests will be carried out in
order to validate the results of the adopted numerical models.
Chapter 6 85
Chapter 6
Dynamic analysis of a pilot plant based on
LHTES system for DSG applications at
Plataforma Solar de Almeria
The work presented in the previous chapters is based on the developed of numerical models to
perform and simulate latent heat thermal energy storage devices. Furthermore, the design and the
implementation of an experimental facility as well as of a shell and tube PCM storage system in
the laboratory of the Department of Mechanical, Chemical and Materials Engineering of the
University of Cagliari were performed.
To better understand the issues related to the experimental facilities based on the LHTES systems,
and to study more in-depth the applications of this technology to real cases, an experimental
investigation was also carried out in collaboration with the research center "PSA-Plataforma Solar
de Almeria" situated in the Tabernas Desert (Province of Almeria, Spain). The Plataforma Solar
de Almería (PSA), a dependency of the Centro de Investigaciones Energéticas, Medioambientales
y Tecnológicas (CIEMAT), is the largest concentrating solar technology research, development
and test center in Europe.
This further work was aimed to the set-up of the test facility implemented in the PSA laboratories
for evaluating PCM-TES systems, and perform modelling and simulation of a complete system.
In addition, the study of the layout, the re-design and modification of the experimental test facility
was realized. Finally, a simplified numerical model to simulate the dynamic behaviour of entire
system during both charge and discharge processes was developed.
This study is part of the REELCOOP project (Renewable Electricity Cooperation,
www.reelcoop.com) of the Seventh European Framework Programme, which involves the
construction of a hybrid solar thermal power plant to produce electricity at the "École Nationale
d'Ingénieurs de Tunis (ENIT)" in Tunisia, with the collaboration of companies from different
European countries. The system is composed of parabolic solar collectors, a biomass boiler and a
thermal energy storage system, while the power section is based on an ORC (Organic Rankine
Cycle) plant. In particular, the CIEMAT had the task of developing the latent heat thermal storage
system, based on the concept of shell and tube heat exchanger, using the steam produced in the
solar collectors and the boiler, as thermo-vector fluid system.
86 Chapter 6
6.1 Introduction
Direct Steam Generation (DSG) in linear Fresnel or parabolic trough collectors is a promising
technology to produce heat and power from solar energy, avoiding the use of thermal oil and thus
decreasing costs [76]. For DSG systems, but in general for all technologies affected by
intermittent availability of energy source, energy storage systems play a fundamental role in
conserving energy reducing the mismatch between energy supply and demand [2,3]. State of the
art parabolic trough power plants use HTF (synthetic oil) and a sensible storage medium (molten
salt). Thus, the energy during charging and discharging can be transferred by a standard heat
exchanger. If water/steam is also used as the primary HTF, the situation becomes more complex.
Indeed while for oil-based CSP plants a 2-tanks molten salt sensible heat storage system has
become a wide-spread standard as reported in Table 6.1 [15], for the DSG solar plants various
system solutions have been proposed, but all of them are still at the pilot plant level technology.
Table 6.1 - Operational solar thermal facilities with thermal energy storage systems.
Among the different proposed solutions, the TES based on configuration of shell and tube heat
exchanger [77][78][79][80], the Multylayer systems [81][82][83][84] and the thermocline with
encapsulated PCM [85] [86] are the most adopted. The configuration of shell and tube heat
exchanger will be further discussed and analyzed in chapter 6.
Chapter 6 87
6.2 Material and method
Figure 6.1 reports the layout of the hybrid solar thermal power plant designed for REELCOOP
project. The red lines represent the steam and blue lines represent the condensate.
Fig. 6.1 - Layout of the hybrid solar thermal power plant (REELCOOP project)
As said before, CIEMAT as partner of this European project, had the task to investigate and
design the storage system of the plant. Thus, the implementation of a test facility in the PSA
laboratories was carried out in order to simulate the operating condition of the storage system
evaluating its thermal performance.
The test facility for thermal energy storage system is composed of a pump that allows the
circulation of the HTF during the charging and discharging processes, an electric boiler to
produce steam (to simulate the solar field), a valve to control the pressure at the electric steam
boiler outlet, the PCM-TES system based on the configuration of shell and tube heat exchanger
and a mixer used as a condenser and considered as the thermal user.
Figures 6.2 and 6.3 show the test facility layout during charge and the discharge process
respectively. During charge phase, the water is heated by the electric boiler until reaching the
operating conditions of saturated steam (through pressure control), and then enters the TES
transferring heat to the PCM material.
88 Chapter 6
Fig. 6.2 - Test facility layout during charge phase
In the discharging phase, the water enters the TES as saturated liquid (at a given pressure) and
receives heat from the PCM material, converting into steam. Subsequently, the water enters the
mixer where it condenses. Red and blue lines represent the HTF in vapor and liquid conditions
respectively that circulates within the pilot plant.
Fig. 6.3 - Test facility layout during discharge phase
TES prototype
MIXER
E-200
P-200
DISSFLASH TANK
TK-14
DISS DEMI WATER
TANK
TK-40
Saturated steam from:
- DISS: up to 30 bar/250oC
- SG: up to 50 bar/300oC
V-1V-3
V-10V-4
V-2
V-23 V-24
V-12
V-5
V-11 V-6
V-7
V-1
6
RV-1
RV
-2
V-26
V-20
V-8
V-19
Cold water from:
- DISS: atmosph. pres/temp
Test facility name:
Description:
Prepared by:
REELCOOP
TES charging process
LVG Date: June 16, 2014
TES prototype
MIXER
E-200
P-200
DISSFLASH TANK
TK-14
DISS DEMI WATER
TANK
TK-40
V-1V-3
V-10V-4
V-2
V-23 V-24
V-12
V-5
V-11 V-6
V-7
V-1
6
RV-1
RV
-2
V-26
V-20
V-8
V-19
Subcooled water from:
- DISS: up to 30 bar/230oC
Cold water from:
- DISS: atmosph. pres/temp
Test facility name:
Description:
Prepared by:
REELCOOP
TES discharging process
LVG Date: June 16, 2014
Chapter 6 89
During charge phase, steam temperature is equal to 180°C while in discharge phase, the steam at
160°C shall be provided to the ORC. For this temperature range D-Mannitol was selected as
PCM. The properties of D-Mannitol have been already shown in Table 4.4.
As part of this project, a dynamic model of the test facility based on latent heat thermal energy
storage system was developed using the commercial softwares Matlab and Simulink.
Circulating pump
The pump was used to circulate the HTF within the plant during both charge and discharge
processes allowing to reach the operating pressure required.
Fig. 6.4 - Pump characteristic curve head-flow
The pump characteristic curve head-flow is reported in Figure 6.4 and from which the Equation
(6.1) is obtained:
ℎ = −0.0157 ∙ 𝑄3 − 0.5639 ∙ 𝑄2 − 0.4148 ∙ 𝑄 + 316.66 (6.1)
The model of the pump is presented in Figure 6.5. The pump extracts the water form a tank
connected to water supply. Water flow rate, temperature and pressure are the model input, while
the operating pressure is the output.
90 Chapter 6
Fig. 6.5 - Circulating pump model
Electric steam boiler and regulating valve
Drum boiler dynamics was extensively studied over the years. Model-based control was the
common method used by the most of research [87]. Wen Tan et al. [88] and [89] designed a linear
controller of a boiler-turbine unit to operate in a carefully selected operating range of a highly
non-linear model. Kim [90] investigated the analysis of the response of a thermal power plant
using optimal control of drum level. Caifen Fu et al. [91] developed a robust PI controller to study
the performance of a benchmark boiler system. Hėctor et al. [92] studied a sliding-mode control
to achieve robust tracking of drum-type steam generating units. Bin Li et al. [93] modelled and
simulated the start-up behaviour of controlled circulation and natural circulation boilers. Heimo
[94] presented a comparison of four finite-volume-algorithms for the dynamic simulation of
natural circulation steam generators. Adam et al. [95] developed a mathematical model for drum
type boilers using a combination of non-linear equations, to describe the evaporation in the
vertical tubes and the phase separation in the steam drum. Zhang et al. [96] studied two phase
flow inside the risers, while Emara-Shabaik et al. [97] introduce a model to predict riser’s
temperature. One of the most complicated task is modelling water level because of the presence of
steam below the liquid level in the drum causes the shrink-and-swell phenomena which makes
level control difficult. Although the level control is very important for safe operation of boilers,
none of the available literature presents a complete model for the system including the drum level.
Kim H. and Choi S. [98] and Åström, K.J. and Bell R.D. [99] presented models to describe the
volume of steam under the water level which can be used indirectly to evaluate the level.
A schematic picture of a boiler system is presented in Fig. 6.6. The heat, Q, supplied to the risers
causes boiling. Feedwater, �̇�𝑓, is supplied from the pump to the drum while saturated steam, �̇�𝑠,
is taken from the drum and sent to the TES system. Drum-type boilers use the principle of natural
water circulation, where the density differences causes circulation of water in the down comer
riser loop. Addition of heat causes the creation of steam bubbles in the riser tubes which are
naturally separated from the saturated water in the drum. The upper part contains saturated steam
while the lower part contains a steam/water mixture.
Chapter 6 91
Fig. 6.6 - Schematic picture of a boiler system [99]
The system can be described by a simplified model only using global mass and energy balances
[99]. The boiler achieves a very efficient heat transfer due to boiling and condensation. All parts
of the system which are in contact with the saturated liquid-vapor mixture will be in thermal
equilibrium. Energy stored in steam and water is released or absorbed very rapidly when the
pressure changes ensuring that different parts of the boiler change their temperature in the same
way. For this reason the dynamics can be captured by models of low order.
The global mass balance is given by Equation 6.2:
𝑑
𝑑𝑡(𝜌𝑠𝑉𝑠 + 𝜌𝑤𝑉𝑤) = �̇�𝑓 − �̇�𝑠 (6.2)
while the global energy is given by Equation 6.3:
𝑑
𝑑𝑡(𝜌𝑠ℎ𝑠𝑉𝑠 + 𝜌𝑤ℎ𝑤𝑉𝑤 − 𝑝𝑉𝑡 +𝑚𝑡,𝑚𝐶𝑝,𝑚𝑇𝑚) = 𝑄 + �̇�𝑓ℎ𝑓 − �̇�𝑠ℎ𝑠 (6.3)
In the reported equations the subscripts 𝑠, 𝑤, 𝑓,𝑚 refer to steam, water, feedwater and metal
respectively, while �̇� represent the mass flow rate, 𝜌 specific density, 𝑉𝑡 total volume , ℎ specific
enthalpy, 𝑇 temperature, 𝑝 pressure, 𝐶𝑝,𝑚 specific heat and 𝑚𝑡 total mass.
The total volume of the drum, downcomer, and risers, 𝑉𝑡 is given by Equation 6.4:
𝑉𝑡 =∗ (𝑉𝑠 + 𝑉𝑤) (6.4)
where 𝑉𝑠 and 𝑉𝑤 represent the total steam and water volumes, respectively. Equations (6.2), (6.3)
and (6.4) are combined with saturated steam tables in order to obtain the boiler model that,
mathematically, represents a differential algebraic system.
�̇�𝑠
�̇�𝑓
Q
92 Chapter 6
Pressure and total volume of water inside the boiler are the state variables from which are derived
the following state equations, used to built the model developed in Simulink environment as
reported in Figure 6.7. Using saturated steam tables, the variables 𝜌𝑠, 𝜌𝑤, ℎ𝑠, and ℎ𝑤 are
expressed as functions of steam pressure.
𝑒11𝑑𝑊𝑤𝑑𝑡
+ 𝑒12𝑑𝑝
𝑑𝑡= �̇�𝑓 − �̇�𝑠 (6.5)
𝑒21𝑑𝑊𝑤𝑑𝑡
+ 𝑒22𝑑𝑝
𝑑𝑡= 𝑄 + �̇�𝑓ℎ𝑓 − �̇�𝑠ℎ𝑠 (6.6)
where:
𝑒11 = 𝜌𝑤 − 𝜌𝑠 (6.7)
𝑒12 = 𝑉𝑤𝜕𝜌𝑤𝜕𝑝
+ 𝑉𝑠𝜕𝜌𝑠𝜕𝑝
(6.8)
𝑒21 = 𝜌𝑤ℎ𝑤 − 𝜌𝑠ℎ𝑠 (6.9)
𝑒22 = 𝑉𝑤 (ℎ𝑤𝜕𝜌𝑤𝜕𝑝
+ 𝜌𝑤𝜕ℎ𝑤𝜕𝑝
)+𝑉𝑠 (ℎ𝑠𝜕𝜌𝑠𝜕𝑝
+ 𝜌𝑠𝜕ℎ𝑠𝜕𝑝) − 𝑉𝑡 +𝑚𝑡𝐶𝑝
𝜕𝑡𝑠𝜕𝑝
(6.10)
This model (Eqs. 6.5-6.10) describes the response of drum pressure to changes in input power,
feedwater flow rate and steam flow rate.
Two PI controllers are used in the system using Cohen-Coon method. Proportional-integral-
derivative (PID) controllers are the main types of feedback control and are widely used in
industry due to their simplicity and easy to tuning. A PID controller calculates an error value as
the difference between a measured process variable and a desired set-point. The output of PID
controller is a linear combination of the input, the derivative of the input and the integral of the
input.
The Cohen-Coon tuning method requires the response of an open-loop system to an input step
change. The response generates a process reaction curve, which can adequately be represented by
a first order system with dead time. From the generated curve, the static gain (Kc), the time
constant (τI ) and the dead time (τD) can all be estimated and used in the rules summarized in
Table 6.2 to find the controller parameters.
Table 6.2- Cohen-Coon Formulas
Controller Type Controller Gain Kc Reset Time τI Derivative Time τD
P 𝐾𝑐 = (1
𝐾𝑝) (𝜏𝑝
𝑡𝑑) (1 +
𝑡𝑑3𝜏𝑝
)
Chapter 6 93
PI 𝐾𝑐 = (
1
𝐾𝑝) (𝜏𝑝
𝑡𝑑) (
9
10+
𝑡𝑑12𝜏𝑝
) 𝜏𝐼 = 𝑡𝑑 (
30 +3𝑡𝑑
𝜏𝑝⁄
9 +20𝑡𝑑
𝜏𝑝⁄)
PID 𝐾𝑐 = (
1
𝐾𝑝) (𝜏𝑝
𝑡𝑑) (4
3+𝑡𝑑4𝜏𝑝
) 𝜏𝐼 = 𝑡𝑑 (
32 +6𝑡𝑑
𝜏𝑝⁄
13 +8𝑡𝑑
𝜏𝑝⁄)
𝜏𝐷 = 𝑡𝑑4
11 +2𝑡𝑑
𝜏𝑝⁄
The controller attempts to minimize the error by adjusting the process through the use of a
manipulated variable. In this case, the first PID controls the outside pressure by manipulating
boiler power. The second PID controls the steam flow rate by manipulated flow coefficient of a
valve situated at the boiler output.
The valve allows adjustment of the inlet pressure to the electric boiler. It is represented by the
Equation 6.11:
�̇� = 𝐾𝑣 ∙ √∆𝑃𝑣 (6.11)
The 𝐾𝑣 coefficient represent the opening degree of the valve and it can assume values between 0
(fully closed valve) and 1 (fully opened valve).
Fig. 6.7 - Model of the boiler implemented in Simulink
Mixer
94 Chapter 6
A mixer (Fig. 6.8) is used to calculate the steam quality of the flow leaving the boiler. This flow is
mixed with a saturated water flow that enters in the mixer with a certain temperature.
Fig. 6.8 - Schematic picture of the mixer
The global mass and energy balances are given by equation 6.12 and 6.13:
�̇�ℎ𝑡𝑓 + �̇�𝑤,𝑖𝑛 = �̇�𝑚𝑖𝑥,𝑜𝑢𝑡 (6.12)
�̇�𝐻𝑇𝐹(𝑡)[ℎ𝐻𝑇𝐹,𝑠𝑥(𝑡) + ℎ𝐻𝑇𝐹,𝑤(1 − 𝑥(𝑡))] + �̇�𝑤,𝑖𝑛(𝑡)ℎ𝑤,𝑖𝑛 = �̇�𝑚𝑖𝑥,𝑜𝑢𝑡(𝑡)ℎ𝑚𝑖𝑥,𝑜𝑢𝑡 (6.13)
where ℎ𝐻𝑇𝐹,𝑠 and ℎ𝐻𝑇𝐹,𝑤 are the specific enthalpies of the HTW in vapor or liquid condition
respectively, functions of the temperature and pressure at boiler outlet. Figure 6.9 reports the
mixer model developed in Simulink environment. The parameter ℎ𝑤,𝑖𝑛 is the specific enthalpy of
the water at the mixer inlet, while ℎ𝑚𝑖𝑥,𝑜𝑢𝑡 is the specific enthalpy of the mixture flow at the
mixer outlet. The temperature 𝑇𝑤,𝑖𝑛 of the water that entering into the mixer is evaluated in order
to achieve the saturated liquid condition of the mixture flow at the mixer outlet.
Chapter 6 95
Fig. 6.9 - Mixer model implemented in Simulink
6.3 Conclusions
In chapter 6 the performance analysis of a test facility based on latent heat thermal energy storage
system was presented. This study was carried out with the collaboration of the research center of
the "PSA-Plataforma Solar de Almeria" in the framework of the European project REELCCOP. A
simplified numerical model was developed using the commercial softwares Matlab and Simulink
to simulate the complete system behaviour (steam generator, a TES system and a cooling system)
during the charge and discharge process of a PCM-TES system. At the time of writing the present
PhD thesis, the plant is still under development.
Program changes and updates of research activity led by project management needs determined
by partnerships between different European subjects, have delayed the implementation and
realization phases of the project. Nevertheless acquired skill and technique have led contributions
on research and experimental activities in the laboratories of the University of Cagliari. In fact,
experimental data will assist in the validation of the model that could be used for future analysis
on the effects of design parameters on the performance of the system. The model will be adapted
to allow the simulation of the test rig designed and implemented in the laboratory for TES
technologies of the DIMCM-University Cagliari presented in Chapter 5.
96 Chapter 7
Chapter 7
Conclusions and future research
Energy storage plays an important roles in conserving available energy and improving its
utilization, since many energy sources are intermittent in nature. Among the different methods
used to store thermal energy, latent heat storage systems, which involve storing and recovery heat
through the solid-liquid transition of phase change materials (PCM), is one of the most attractive
option. These systems have various advantages with respect the others: the latent heat of most
materials is much higher than their sensible heat, thus requiring a smaller mass of storage medium
to storing/recovering a given amount of thermal energy with a consequent reduction of costs; the
phase change process occurs at a nearly constant temperature, which is a fundamental aspect for
efficient operation of most thermal systems.
In this framework, the investigation of thermal energy storage systems based on latent heat
concept for renewable energy and other non programmable energy sources, industrial processes
and heat and power generation for intermediate temperature applications (150-250 °C) was
carried out. Main objective of this work is framed in the analysis of the performance of PCM-TES
devices with respect to energy stored/released, time and efficiency during repeated cycles of
charge/discharge, the analysis on different materials, geometries and heat transfer enhancement
techniques in order to optimize the entire process. This work is based on two parts: the first part
concerns the development of numerical models for simulating the transient behaviour of the
PCM-TES, to predict the energy balance in space and time and the TES overall performances and
their application to several test cases. The second part concerns the design and the implementation
of a test rig specifically built for experimental investigation of heat storage devices.
These models were developed using 2D and 3D numerical simulation codes specifically
implemented in the COMSOL Multiphysics environment. Two different approaches were
analyzed to perform the behavior of PCM during phase transition. The first approach considers
heat transfer only by conduction in both solid and liquid PCM phases. The second approach
considers heat transfer by conduction and natural convection in liquid PCM domain. To model the
phase transition, the apparent heat capacity formulation was used in both approaches. In this
method, the latent heat was implemented by increasing the heat capacity of the material, while the
phase change process was modelled by assuming that the transition takes place in a narrow range
of temperature rather than at a fixed temperature. The two approaches were separately evaluated
for two different cases and then were validated by comparing the numerical results with
experimental data. For each model temperature behavior, phase change evolution and melting
fraction were evaluated and analyzed for both charge and discharge processes.
The numerical codes, adopted to different PCM materials and TES geometries prove to be
suitable for the simulation of the latent heat thermal energy storage systems. Furthermore, the
numerical results demonstrate a good agreement with the experimental result for both approaches,
also showing that the second approach was more accurate. Main differences between them
concern the shape and the motion of solid-liquid interface were evaluated during transition
Chapter 6 97
process. These two aspects depend on the heat transfer process considered. In fact, in melting
process the heat transfer is dominated by convection, while in solidification process the heat
transfer is dominated by conduction. Considering first approach, the solid-liquid interface moves
uniformly around an heat source surface, while in the second approach, natural convection and
buoyancy force cause a change of the shape of the melting/solidification front.
First approach was used to simulate a PCM-TES device based on the configuration of a shell and
tube heat exchanger using Hydroquinone as PCM material. The results obtained showed that the
PCM nearest to the shell was the last that undergoes the transition in both charge and discharge
phases. With the first approach, the convection and the buoyancy force in liquid PCM domain
were not considered, so the solid-liquid interface moves around the tubes uniformly.
Second approach was used to perform a comparison between three different storage devices, a
double tube heat exchanger (Case 1), a triplex heat exchanger (Case 2) and a triplex with finned
surfaces (Case 3), using D-Mannitol as PCM. These systems were used to determine which
configurations are capable of enhancing thermal response between heat source and a PCM. As
expected, the Case 2 and Case 3 were the solutions that allowed the faster response of the TES
device during the charge and discharge processes. The insertion of fins allowed, in particular, not
only an increase in the heat exchange surface of the inner HTF tube, but also the creation of cells
in the PCM volume that determined faster melting/solidification of the PCM. Furthermore, it was
found that the different configurations of this three systems considered have a strong impact on
the shape of melting-solidification front as well as natural convection and buoyancy forces. In
Case 1 the solid-liquid interface moves parallel and radially from the centre to the wall of the TES
but it slopes gradually from the top. In Case 2 the interface assumed a monotonic shape, while in
Case 3 various cells with liquid PCM formed during the process.
Furthermore, the effect of the number of fins on the melting rate was investigated comparing five
different cases (0, 2, 4, 6, 8 fins). A big influence of the fins number on reducing the melting time
was found. Considering the 85% of total melting, a reduction of 18.6% of melting time was
estimated for the case with 8 fins with respect to the case without fins. The relative percentage
difference of melting time ΔMT% presents a maximum value of -7.2% for TES with four fins,
while for higher number of fins this parameter decreases. Whereby, on the one hand the fins
increased heat transfer rate by increasing the total surface area available for heat transfer by
conduction, on the other high number of fins reduces the formation of convective cells decreasing
the amount of heat transfer by convection.
Finally, the validation of these two methods was carried out using a storage system based on the
configuration of a double tube with finned surfaces and paraffin as PCM. In order to evaluate
which one of the two proposed approaches show more accuracy during charge and discharge
processes, a comparison with the results obtained with two experimental tests, with different HTF
flow rate values, was carried out. These tests were performed in the laboratories of the research
center GREA Innovació Concurrent (University of Lleida, Spain). Overall, a good agreement with
the experimental temperature profiles during charge and discharge phase was obtained. However,
it was found that heat transfer mode influences the interface shape and motion during both the
melting and solidification processes. In fact, natural convection in melt region drives and
improves the heat transfer rate increasing the velocity of the solid-liquid interface. At the end of
charge phase, the temperature profile obtained with the second approach shows a good agreement
with respect to the experimental results, while the first approach is less accurate. Instead, the
numerical prediction of both approaches appears very similar to the experimental results during
discharge process. Same considerations for melting fraction. Comparing the melting fraction
98 Chapter 7
values, a difference of 0.14 and 0.2 between second and first approach were obtained for
experiment 1 and 2 respectively at the end of charge process, while a difference of 0.04 was
obtained for both experiments at the end of discharge phase. Considering the solid-liquid
interface, it can be noticed that it moves parallel and radially from the centre to the wall of the
TES in the first approach, while in the second approach, due to natural convection and buoyancy
force, this boundary slopes gradually from the top, inward during melting and outward during
solidification.
Finally, the first approach was simple and required relatively low computational resources but it
was proven less accurate. A good agreement was obtained using the second approach that was
more closer to the experimental results thus, natural convection plays a significant role in phase
change process and it must be taken into account. The effects of natural convection on the shape
and the motion of solid-liquid interface can not be neglected. However, it must be considered that
the addition of natural convection implies a major requirement of computational resources.
The second part, as said before, concerns the design and the implementation of a test rig
specifically built for experimental investigation of heat storage devices. The test rig, now
implemented in the laboratory for TES technologies of the Department of Mechanical, Chemical
and Materials Engineering (DIMCM) of the University of Cagliari, was conceived and designed
not only to validate all the developed numerical models, but also to carry out a considerable
research activity in the field of thermal energy storage based on modeling, control and testing of
innovative TES systems for industrial applications. The experimental facility is composed of an
electrical heater, a pump, an aircooler and a thermal energy storage system accurately selected for
the specific application. It allows to operate at a maximum temperature and pressure conditions
up to 350 °C and 15 bar respectively. A PCM-TES prototype was specially designed and build as
latent heat thermal energy storage device based on the configuration of shell and tube heat
exchanger. The design was carried out by means of iterative technique using a LMTD method. At
the time of writing the test rig is already build while the storage system is still under construction.
In future works, a new 3D numerical model based on the configuration of the PCM-TES build for
the test rig using second approach (i.e. natural convection and buoyancy force) will be developed.
Moreover, the analysis and simulation with different geometries and configuration of the storage
systems and the study of others PCM materials will be carried out. Further analysis will be based
on the optimization with respect to the number, the pitch, the thickness, the length and the shape
of the fins, as well as the effects of different flow rate and fins number on the TES thermal
performance will be studied. Finally, an accurate both numerical and experimental investigation
on partial load condition will be carried out in order to study the behaviour and the thermal
performance of PCM-TES under this fundamental aspect regarding most of industrial
applications.
Concerning the experimental facility, the implementation of the PCM-TES device will be carried
out in the short term. Then, the implementation of data acquisition system will be realized in order
to complete the test rig and start the experimental tests.
Chapter 6 99
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